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89件あるらしい。うち１件（１８番）はwithdraw。よって88件。

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https://qiita.com/kaizen_nagoya/items/a9a412561caee3852d77

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https://qiita.com/kaizen_nagoya/items/2b2fe08b5824c6c3c68d

1

Perspectives of quantum annealing: Methods and implementations
Authors: Philipp Hauke, Helmut G. Katzgraber, Wolfgang Lechner, Hidetoshi Nishimori, William D. Oliver
https://arxiv.org/abs/1903.06559 (Submitted on 15 Mar 2019)
Quantum Physics (quant-ph)

[1] Kielpinski D, Monroe C and Wineland D J 2002 Nature 417 709
[2] Blais A, Huang R S, Wallraff A, Girvin S M and Schoelkopf R J 2004 Physical Review A 69 062320
[3] Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S M and Schoelkopf R J 2004 Nature 431 162
[4] Schoelkopf R and Girvin S 2008 Nature 451 664
[5] Clarke J and Wilhelm F K 2008 Nature 453 1031
[6] Bakr W S, Gillen J I, Peng A, F ̈olling S and Greiner M 2009 Nature 462 74
[7] Ladd T D, Jelezko F, Laflamme R, Nakamura Y, Monroe C and O’Brien J L 2010 Nature 464 45
[8] OConnell A D, Hofheinz M, Ansmann M, Bialczak R C, Lenander M, Lucero E, Neeley M, Sank D, Wang H, Weides M et al. 2010 Nature 464 697
[9] Chow J, DiCarlo L, Gambetta J, Nunnenkamp A, Bishop L S, Frunzio L, Devoret M, Girvin S
and Schoelkopf R 2010 Physical Review A 81 062325
[10] Blatt R and Roos C F 2012 Nature Physics 8 277
[11] Cirac J I and Zoller P 2012 Nature Physics 8 264
[12] Yan F, Gustavsson S, Kamal A, Birenbaum J, Sears A, Hover D, Gudmundsen T, Rosenberg
D, Samach G, Weber S, Yoder J, Orlando T, Clarke J, Kerman A and Oliver W 2016 Nature Communications 7 12303
[13] Bernien H, Schwartz S, Keesling A, Levine H, Omran A, Pichler H, Choi S, Zibrov A S, Endres
M, Greiner M et al. 2017 Nature 551 579
[14] Preskill J 2018 Quantum 2 79
[15] Hauke P, Cucchietti F M, Tagliacozzo L, Deutsch I and Lewenstein M 2012 Rep. Prog. Phys. 75 082401
[16] Georgescu I M, Ashhab S and Nori F 2014 Rev. Mod. Phys. 86 153
[17] Peng W, Wang B, Hu F, Wang Y, Fang X, Chen X and Wang C 2019 Science China Physics, Mechanics and Astronomy 62 060311
[18] Kadowaki T and Nishimori H 1998 Phys. Rev. E 58 5355–5363 URL http://link.aps.org/doi/10.1103/PhysRevE.58.5355
[19] Farhi E, Goldstone J, Gutmann S and Sipser M 2000 Quantum Computation by Adiabatic Evolution arXiv:quant-ph/0001106
[20] Kadowaki T 1998 Study of Optimization Problems by Quantum Annealing Ph.D. thesis Tokyo Institute of Technology (quant-ph/0205020)
[21] Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A and Preda D 2001 Science 292 472–475 [22] Neven H, Denchev V S, Rose G and Macready W G 2009 arXiv preprint arXiv:0912.0779
[23] Babbush R, Love P J and Aspuru-Guzik A 2014 Scientific reports 4 6603
[24] Lloyd S, Mohseni M and Rebentrost P 2013 arXiv preprint arXiv:1307.0411
[25] Garnerone S, Zanardi P and Lidar D A 2012 Physical review letters 108 230506
[26] Perdomo-Ortiz A, Dickson N, Drew-Brook M, Rose G and Aspuru-Guzik A 2012 Scientific reports 2 571
[27] Lucas A 2014 Front. Physics 12 5
[28] Binder K and Young A P 1986 Rev. Mod. Phys. 58 801
[29] Young A P (ed) 1998 Spin Glasses and Random Fields (Singapore: World Scientific)
[30] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford, United Kingdom: Oxford University Press)
[31] M ́ezard M, Parisi G and Virasoro M A 1987 Spin Glass Theory and Beyond (Singapore: World Scientific)
[32] Messiah A 1961 Quantum mechanics (Amsterdam, The Netherlands: North-Holland)
[33] Amin M H S 2009 Physical Review Letters 102 220401 ISSN 0031-9007 URL https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.102.220401http://arxiv.org/abs/0810.4335v1{%}5Cnpapers2://publication/uuid/4E8D7E3F-DB05-4D52-8EC6-039C1353944B
[34] Jansen S, Ruskai M B and Seiler R 2007 Journal of Mathematical Physics 48 102111 ISSN 00222488 URL http://link.aip.org/link/JMAPAQ/v48/i10/p102111/s1{&}Agg=doi
[35] Lidar D a, Rezakhani A T and Hamma A 2009 Journal of Mathematical Physics 50 102106 ISSN 00222488 URL http://scitation.aip.org/content/aip/journal/jmp/50/10/10.1063/1.
3236685
[36] Cheung D, Høyer P and Wiebe N 2011 Journal of Physics A: Mathematical and Theoretical 44 415302 ISSN 1751-8113 URL http://stacks.iop.org/1751-8121/44/i=41/a=415302?key=crossref.91f0afd8808f52d028b8ac76a3989a72
[37] Bunyk P, Hoskinson E, Johnson M W, Tolkacheva E, Altomare F, Berkley A J, Harris R, Hilton J P, Lanting T and Whittaker J 2014 IEEE Trans. Appl. Supercond. 24 1
[38] Johnson M W, Amin M H S, Gildert S, Lanting T, Hamze F, Dickson N, Harris R, Berkley A J, Johansson J, Bunyk P, Chapple E M, Enderud C, Hilton J P, Karimi K, Ladizinsky E, Ladizinsky N, Oh T, Perminov I, Rich C, Thom M C, Tolkacheva E, Truncik C J S, Uchaikin S, Wang J, Wilson B and Rose G 2011 Nature 473 194
[39] Dickson N G, Johnson M W, Amin M H, Harris R, Altomare F, Berkley A J, Bunyk P, Cai J, Chapple E M, Chavez P, Cioata F, Cirip T, Debuen P, Drew-Brook M, Enderud C, Gildert S, Hamze F, Hilton J P, Hoskinson E, Karimi K, Ladizinsky E, Ladizinsky N, Lanting T, Mahon T, Neufeld R, Oh T, Perminov I, Petroff C, Przybysz A, Rich C, Spear P, Tcaciuc A, Thom M C, Tolkacheva E, Uchaikin S, Wang J, Wilson A B, Merali Z and Rose G 2013 Nat. Commun. 4 1903
[40] Weber S, Samach G, Hover D, Gustavsson S, Kim D, Melville A, Rosenberg D, Sears A, Yan F, Yoder J, Oliver W and Kerman A 2017 Phys. Rev. Applied 8 014004
[41] Rosenberg D, Kim D, Das R, Yost D, Gustavsson S, Hover D, Krantz P, Melville A, Racz L, Samach G, Weber S, Yan F, Yoder J, Kerman A and Oliver W 2017 npj Quantum Information 3 42
[42] Albash T and Lidar D A 2018 Phys. Rev. X 8 031016
[43] Katzgraber H G, Hamze F and Andrist R S 2014 Phys. Rev. X 4 021008
[44] Rønnow T F, Wang Z, Job J, Boixo S, Isakov S V, Wecker D, Martinis J M, Lidar D A and Troyer M 2014 Science 345 420–424
[45] Katzgraber H G, Hamze F, Zhu Z, Ochoa A J and Munoz-Bauza H 2015 Phys. Rev. X 5 031026 [46] Hen I, Job J, Albash T, Rønnow T F, Troyer M and Lidar D A 2015 Phys. Rev. A 92 042325 [47] King A D, Lanting T and Harris R 2015 Performance of a quantum annealer on range-limited
constraint satisfaction problems arXiv:1502.02098
[48] Mandr $'a$ S, Zhu Z, Wang W, Perdomo-Ortiz A and Katzgraber H G 2016 Phys. Rev. A 94 022337
[49] Mandr $'a$ S and Katzgraber H G 2017 Quantum Sci. Technol. 2 038501
[50] Mandr $'a$ S and Katzgraber H G 2018 Quantum Sci. Technol. 3 04LT01
[51] Altshuler B, Krovi H and Roland J 2010 PNAS 107 12446
[52] Boixo S, Rønnow T F, Isakov S V, Wang Z, Wecker D, Lidar D A, Martinis J M and Troyer M
2014 Nat. Phys. 10 218
[53] Rønnow T F, Wang Z, Job J, Boixo S, Isakov S V, Wecker D, Martinis J M, Lidar D A and
Troyer M 2014 Science 345 420–424
[54] Katzgraber H G 2018 Viewing vanilla quantum annealing through spin glasses
URL http://stacks.iop.org/2058-9565/3/i=3/a=030505?key=crossref.77e4319dbac662ec3c164f9d634cce58
[55] Isakov S V, Mazzola G, Smelyanskiy V N, Jiang Z, Boixo S, Neven H and Troyer M 2016 Physical review letters 117 180402
[56] Andriyash E and Amin M H 2017 arXiv:1703.09277 1–12 URL http://arxiv.org/abs/1703. 09277
[57] Bravyi S and Terhal B 2009 SIAM J. Comput. 39 1462 ISSN 0895-4798 URL http://epubs. siam.org/doi/10.1137/090750688
[58] Albash T and Lidar D A 2018 Rev. Mod. Phys. 90 015002 URL https://link.aps.org/doi/ 10.1103/RevModPhys.90.015002
[59] Das A and Chakrabarti B K 2008 Rev. Mod. Phys. 80 1061
[60] Venegas-Andraca S E, Cruz-Santos W, McGeoch C and Lanzagorta M 2018 Contemporary Physics
59 174–197 ISSN 13665812 URL https://doi.org/10.1080/00107514.2018.1450720
[61] Venturelli D, Mandr$'a$ S, Knysh S, O’Gorman B, Biswas R and Smelyanskiy V 2015 Phys. Rev. X 5 031040
[62] Perdomo-Ortiz A, Dickson N, Drew-Brook M, Rose G and Aspuru-Guzik A 2012 Sci. Rep. 2 571 [63] Perdomo-Ortiz A, Fluegemann J, Narasimhan S, Biswas R and Smelyanskiy V N 2015 Eur. Phys. J., Special Topics 224 131
[64] Perdomo-Ortiz A, Feldman A, Ozaeta A, Isakov S V, Zhu Z, O’Gorman B, Katzgraber H G,
Diedrich A, Neven H, de Kleer J, Lackey B and Biswas R 2017 arXiv preprint arXiv:1708.09780 ArXiv:1708.09780
[65] Rieffel E G, Venturelli D, O’Gorman B, Do M B, Prystay E M and Smelyanskiy V N 2015 Quant. Inf. Proc. 14 1
[66] Venturelli D, Marchand D J J and Rojo G 2015 arXiv preprint arXiv:1506.08479 (arxiv:1506.08479)
[67] Benedetti M, Realpe-G ́omez J, Biswas R and Perdomo-Ortiz A 2016 arXiv preprint arXiv:1609.02542 (arxiv:1609.02542)
[68] Hernandez M and Aramon M 2017 Quantum Information Processing 16 133
[69] Rosenberg G, Haghnegahdar P, Goddard P, Carr P, Wu K and de Prado M L 2016 IEEE Journal of Selected Topics in Signal Processing 10 1053
[70] Stein D L and Newman C M 2013 Spin Glasses and Complexity Primers in Complex Systems (Princeton NJ: Princeton University Press)
[71] Katzgraber H G and Young A P 2003 Phys. Rev. B 68 224408
[72] Katzgraber H G, K ̈orner M, Liers F, Ju ̈nger M and Hartmann A K 2005 Phys. Rev. B 72 094421 [73] Zhu Z, Fang C and Katzgraber H G 2016 borealis - A generalized global update algorithm for Boolean optimization problems (arXiv:1605.09399)
[74] Knysh S 2016 Nature Communications 7 12370 ISSN 2041-1723 URL http://www.nature.com/doifinder/10.1038/ncomms12370
[75] Choi V 2008 Quantum Inf. Process. 7 193
[76] Zaribafiyan A, Marchand D J J and Changiz Rezaei S S 2017 Quantum Information Processing 16 1–26 ISSN 15700755
[77] Lechner W, Hauke P and Zoller P 2015 Science advances 1 e1500838
[78] Rocchetto A, Benjamin S C and Li Y 2016 Science advances 2 e1601246
[79] Leib M, Zoller P and Lechner W 2016 Quantum Science and Technology 1 015008
[80] Goto H 2015 Scientific reports 6 21686 ISSN 2045-2322 URL http://arxiv.org/abs/1510.02566http://dx.doi.org/10.1038/srep21686
[81] Puri S, Andersen C K, Grimsmo A L and Blais A 2017 Nature communications 8 15785
[82] Chancellor N, Zohren S and Warburton P A 2017 npj Quantum Information 3 21
[83] Glaetzle A W, van Bijnen R M, Zoller P and Lechner W 2017 Nature Communications 8 15813 [84] https://www.dwavesys.com/
[85] Marzlin K P and Sanders B 2004 Physical Review Letters 93 160408 ISSN 0031-9007 URL http://link.aps.org/doi/10.1103/PhysRevLett.93.160408
[86] Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A and Preda D 2001 Science 292 472–476 [87] Aharonov D, van Dam W, Kempe J, Landau Z, Lloyd S and Regev O 2008 SIAM Review 50 755–787 ISSN 0036-1445 URL http://www.siam.org/journals/ojsa.phphttp://epubs.
siam.org/doi/10.1137/080734479
[88] Biamonte J and Love P 2008 Physical Review A 78 012352 ISSN 1050-2947 URL http://link.aps.org/doi/10.1103/PhysRevA.78.012352
[89] 1988 Proceedings of the Ascona/Locarno Conference (World Scientific)
[90] Apolloni B, Carvalho C and de Falco D 1989 Stochastic Process and their applications 33 233–244 [91] Finnila A B, Gomez M A, Sebenik C, Stenson C and Doll J D 1994 Chemical Physics Letters 219 343–348
[92] Amara P, Hsu D and Straub J 1993 The Journal of Physical Chemistry 97 6715–6721 ISSN 0022-3654 URL http://pubs.acs.org/doi/abs/10.1021/j100127a023
[93] Tanaka K and Horiguchi T 2000 Electronic and Communications in Japan 83 84–94
[94] Sachdev S 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press)
[95] Cabrera G G and Jullien R 1987 Physical Review B 35 7061
[96] Laumann C R, Moessner R, Scardicchio A and Sondhi S L 2012 Physical Review Letters 109 030502 ISSN 00319007 URL https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.109.030502
[97] Tsuda J, Yamanaka Y and Nishimori H 2013 Journal of the Physical Society of Japan 82 114004 [98] Nishimori H and Ortiz G 2011 Elements of Phase Transitions and Critical Phenomena (Oxford, United Kingdom: Oxford University Press)
[99] Lishan Zeng Jun Zhang M S 2015 J. Phys. A: Math. Theor. 49 165305
[100] Susa Y, Yamashiro Y, Yamamoto M and Nishimori H 2018 Journal of the Physical Society of Japan 87 023002 ISSN 0031-9015 URL http://arxiv.org/abs/1801.02005 http://journals.jps.jp/doi/10.7566/JPSJ.87.023002
[101] Susa Y, Yamashiro Y, Yamamoto M, Hen I, Lidar D A and Nishimori H 2018 arXiv:1808.01582 URL http://arxiv.org/abs/1808.01582
[102] McGeoch C C 2012 A Guide to Experimental Algorithmics (Cambride, UK: Cambridge University Press)
[103] Rønnow T F, Wang Z, Job J, Boixo S, Isakov S V, Wecker D, Martinis J M, Lidar D A and Troyer M 2014 Science 345 420
[104] Matsuda Y, Nishimori H and Katzgraber H G 2009 New J. Phys. 11 073021
[105] Mandr$'a$ S, Zhu Z and Katzgraber H G 2017 Phys. Rev. Lett. 118 070502
[106] Santoro G, Martonˇ ́ak R Tosatti E and Car R 2002 Science 295 2427
[107] Santoro G E and Tosatti E 2006 J. Phys. A 39 R393
[108] Pudenz K L, Albash T and Lidar D A 2014 Nat. Commun. 5 3243
[109] Smith G and Smolin J 2013 Physics 6 105
[110] Boixo S, Albash T, Spedalieri F M, Chancellor N and Lidar D A 2013 Nat. Commun. 4 2067 [111] Lanting T, Przybysz A J, Smirnov A Y, Spedalieri F M, Amin M H, Berkley A J, Harris R, Altomare F, Boixo S, Bunyk P, Dickson N, Enderud C, Hilton J P, Hoskinson E, Johnson M W, Ladizinsky E, Ladizinsky N, Neufeld R, Oh T, Perminov I, Rich C, Thom M C, Tolkacheva E, Uchaikin S, Wilson A B and Rose G 2014 Phys. Rev. X 4 021041
[112] Santra S, Quiroz G, Ver Steeg G and Lidar D A 2014 New J. Phys. 16 045006
[113] Shin S W, Smith G, Smolin J A and Vazirani U 2014 How “Quantum” is the D-Wave Machine? (arXiv:1401.7087)
[114] Albash T, Vinci W, Mishra A, Warburton P A and Lidar D A 2015 Phys. Rev. A 91 042314 [115] Albash T, Rønnow T F, Troyer M and Lidar D A 2015 Eur. Phys. J. Spec. Top. 224 111
[116] Martin-Mayor V and Hen I 2015 Unraveling Quantum Annealers using Classical Hardness (arXiv:1502.02494)
[117] Pudenz K L, Albash T and Lidar D A 2015 Phys. Rev. A 91 042302
[118] Vinci W, Albash T, Paz-Silva G, Hen I and Lidar D A 2015 Phys. Rev. A 92 042310
[119] Zhu Z, Ochoa A J, Hamze F, Schnabel S and Katzgraber H G 2016 Phys. Rev. A 93 012317 [120] King J, Yarkoni S, Raymond J, Ozfidan I, King A D, Nevisi M M, Hilton J P and McGeoch C C
2019 Journal of the Physical Society of Japan 88 061007
[121] Marshall J, Martin-Mayor V and Hen I 2016 Phys. Rev. A 94 012320
[122] Denchev V S, Boixo S, Isakov S V, Ding N, Babbush R, Smelyanskiy V, Martinis J and Neven
H 2016 Phys. Rev. X 6 031015
[123] Matsubara, Satoshi and Tamura, Hirotaka and Takatsu, Motomu and Yoo, Danny and Vatankhahghadim, Behraz and Yamasaki, Hironobu and Miyazawa, Toshiyuki and Tsukamoto, Sanroku and Watanabe, Yasuhiro and Takemoto, Kazuya and Sheikholeslami, Ali 2017 Ising-Model Optimizer with Parallel-Trial Bit-Sieve Engine (Cham: Springer International Publishing) p 432
[124] Aramon M, Rosenberg G, Miyazawa T, Tamura H and Katzgraber H G 2018 arXiv preprint arXiv:1806.08815 (arXiv:1806.08815)
[125] Geyer C 1991 Monte Carlo Maximum Likelihood for Dependent Data 23rd Symposium on the Interface ed Keramidas E M (Fairfax Station, VA: Interface Foundation) p 156
[126] Hukushima K and Nemoto K 1996 J. Phys. Soc. Jpn. 65 1604
[127] Houdayer J 2001 Eur. Phys. J. B. 22 479
[128] Zhu Z, Ochoa A J and Katzgraber H G 2015 Phys. Rev. Lett. 115 077201
[129] Hamze F and de Freitas N 2004 From Fields to Trees Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence UAI ’04 (Arlington, Virginia, United States: AUAI Press) p 243 ISBN 0-9749039-0-6
[130] Selby A 2014 Efficient subgraph-based sampling of Ising-type models with frustration (arXiv:cond-mat/1409.3934)
[131] Kirkpatrick S, Gelatt, Jr C D and Vecchi M P 1983 Science 220 671
[132] Hukushima K and Iba Y 2003 Population Annealing and Its Application to a Spin Glass The Monte Carlo method in the physical sciences: celebrating the 50th anniversary of the Metropolis
algorithm vol 690 ed Gubernatis J E (Los Alamos, New Mexico (USA): AIP) p 200
[133] Machta J 2010 Phys. Rev. E 82 026704
[134] Wang W, Machta J and Katzgraber H G 2015 Phys. Rev. E 92 013303
[135] Wang W, Machta J and Katzgraber H G 2015 Phys. Rev. E 92 063307
[136] Hartmann A K and Rieger H 2001 Optimization Algorithms in Physics (Berlin: Wiley-VCH) [137] Elf M, Gutwenger C, Ju ̈nger M and Rinaldi G 2001 Lecture notes in computer science 2241 Computational Combinatorial Optimization vol 2241 ed Ju ̈nger M and Naddef D (Heidelberg: Springer Verlag)
[138] Hartmann A K and Rieger H 2004 New Optimization Algorithms in Physics (Berlin: Wiley-VCH) [139] Gisin N, Ribordy G, Tittel W and Zbinden H 2002 Reviews of modern physics 74 145
[140] Pezz$'e$ L, Smerzi A, Oberthaler M K, Schmied R and Treutlein P 2018 Reviews of Modern Physics 90 035005
[141] Lanting T, King A D, Evert B and Hoskinson E 2017 Phys. Rev. A 96 042322 ISSN 2469-9926 URL https://link.aps.org/doi/10.1103/PhysRevA.96.042322
[142] Albash T, Rønnow T F, Troyer M and Lidar D A 2015 The European Physical Journal Special Topics 224 111–129
[143] Batle J, Ooi C R, Farouk A, Abutalib M and Abdalla S 2016 Quantum Information Processing 15 3081–3099
[144] Hauke P, Bonnes L, Heyl M and Lechner W 2015 Front. Phys. 3 21
[145] Bauer B, Wang L, Piˇzorn I and Troyer M 2015 arXiv:1501.06914 URL http://arxiv.org/abs/1501.06914
[146] Bravyi S, Divincenzo D P, Oliveira R and Terhal B M 2004 Quantum Information and Computation 8 361–385 ISSN 0097-5397 URL http://www.rintonpress.com/xxqic8/ qic-8-5/0361-0385.pdfhttp://arxiv.org/abs/quant-ph/0406180
[147] Klassen J and Terhal B M 2018 arXiv:1806.05405 URL http://arxiv.org/abs/1806.05405 [148] Marvian M, Lidar D A and Hen I 2018 arXiv:1802.03408 URL http://arxiv.org/abs/1802.03408
[149] Hastings M B and Freedman M H 2013 Quantum Information and Computation 13 1038–1076 URL http://arxiv.org/abs/1302.5733
[150] Jarret M, Jordan S P and Lackey B 2016 Physical Review A - Atomic, Molecular, and Optical Physics 94 ISSN 10941622
[151] Landau D P and Binder K 2000 A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge, United Kingdom: Cambridge University Press)
[152] Loh E Y, Gubernatis J E, Scalettar R T, White S R, Scalapino D J and Sugar R L 1990 Physical Review B 41 9301–9307 ISSN 01631829
[153] Troyer M and Wiese U J 2005 Physical Review Letters 94 170201 URL https://journals.aps. org/prl/pdf/10.1103/PhysRevLett.94.170201
[154] Somma R, Nagaj D and Kieferov ́a M 2012 Physical Review Letters 109 050501 ISSN 0031-9007 URL http://link.aps.org/doi/10.1103/PhysRevLett.109.050501
[155] Fujii K 2018 arXiv:1803.09954 URL http://arxiv.org/abs/1803.09954
[156] Seki Y and Nishimori H 2012 Physical Review E 85 051112 ISSN 1539-3755 URL http://link.aps.org/doi/10.1103/PhysRevE.85.051112
https://arxiv.org/pdf/1203.2418.pdf
[157] Seoane B and Nishimori H 2012 Journal of Physics A: Mathematical and Theoretical 45 435301 ISSN 1751-8113 URL http://stacks.iop.org/1751-8121/45/i=43/a=435301?key= crossref.a9016f5faf3414182a13dae40c6cdfe3
[158] Seki Y and Nishimori H 2015 Journal of Physics A: Mathematical and Theoretical 48 335301 URL http://dx.doi.org/10.1088/1751-8113/48/33/335301
[159] Nishimori H and Takada K 2017 Frontiers in ICT 4 2 ISSN 2297-198X URL http://arxiv.org/abs/1609.03785 http://journal.frontiersin.org/article/10.3389/fict.2017.00002/full
[160] J ̈org T, Krzakala F, Kurchan J, Maggs a C and Pujos J 2010 EPL (Europhysics Letters) 89 40004 ISSN 0295-5075 URL http://stacks.iop.org/0295-5075/89/i=4/a=40004?key=crossref.8f005a7bf04ecc43b292fb9797ba7892
[161] Durkin G A 2018 arXiv:1806.07602 1–21 URL http://arxiv.org/abs/1806.07602
[162] Ohzeki M 2017 Scientific Reports 7 41186 ISSN 2045-2322 URL http://arxiv.org/abs/1612.04785
[163] Hormozi L, Brown E W, Carleo G and Troyer M 2017 Physical Review B 95 184416 URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.184416
[164] Albash T 2018 arXiv:1811.09980 URL https://arxiv.org/abs/1811.09980
[165] Zurek W H and Dorner U 2008 Phil. Trans. Roy. Soc. A 366 2953–2972 ISSN 1364-503X URL
http://rsta.royalsocietypublishing.org/cgi/doi/10.1098/rsta.2008.0069
[166] Dziarmaga J and Rams M M 2010 New J. Phys. 12 055007 URL http://stacks.iop.org/1367-2630/12/i=5/a=055007?key=crossref.27e88b11281844ce35986ea51f9ff980
[167] Rams M M, Mohseni M and del Campo A 2016 New J. Phys. 18 123034
[168] Mohseni M, Strumpfer J and Rams M M 2018 arXiv:1804.11037 URL http://arxiv.org/abs/1804.11037
[169] Kibble T W B 1976 Journal of Physics A: Mathematical and General 9 1387–1398 ISSN 0305-4470 URL http://stacks.iop.org/0305-4470/9/i=8/a=029?key=crossref. fd6da1d908a3bf72b56557edd8d38c37
[170] Zurek W H 1985 Nature 317 505–508 URL http://www.nature.com/doifinder/10.1038/ 317505a0
[171] Farhi E, Goldstone J, Gosset D, Gutmann S, Meyer H B and Shor P 2011 Quant. Inf. Proc. 11 181
[172] Dickson N G and Amin M H S 2011 Phys. Rev. Lett. 106 050502 URL https://link.aps.org/ doi/10.1103/PhysRevLett.106.050502
[173] Dickson N G and Amin M H 2012 Phys. Rev. A 85 032303 URL https://link.aps.org/doi/ 10.1103/PhysRevA.85.032303
[174] Adame J I and Mcmahon P L 2018 arXiv:1806.11091 URL https://arxiv.org/abs/1806. 11091
[175] Perdomo-Ortiz A, Venegas-Andraca S E and Aspuru-Guzik A 2010 Quantum Information Processing 10 33–52 ISSN 1570-0755 URL http://www.springerlink.com/index/10.1007/ s11128-010-0168-z
[176] Chancellor N 2017 New Journal of Physics 19 ISSN 13672630 URL https://doi.org/10.1088/ 1367-2630/aa59c4
[177] Ohkuwa M, Nishimori H and Lidar D A 2018 Physical Review A 98 022314 URL https://journals.aps.org/pra/pdf/10.1103/PhysRevA.98.022314http://arxiv.org/ abs/1806.02542
[178] Demirplak M and Rice S A 2003 The Journal of Physical Chemistry A 107 9937–9945
[179] Demirplak M and Rice S A 2005 The Journal of Physical Chemistry B 109 6838–6844
[180] Berry M 2009 Journal of Physics A: Mathematical and Theoretical 42 365303
[181] Sels D and Polkovnikov A 2017 Proc. Natl. Acad. Sci. 114 3909 ISSN 0027-8424 URL http://www.pnas.org/content/early/2017/04/26/1619826114
[182] Takahashi K 2013 Physical Review E 87 062117 ISSN 1539-3755 URL http://link.aps.org/doi/10.1103/PhysRevE.87.062117
[183] del Campo A 2013 Physical review letters 111 100502
[184] Deffner S, Jarzynski C and del Campo A 2014 Physical Review X 4 021013
[185] Torrontegui E, Ib ́anez S, Mart ́ınez-Garaot S, Modugno M, del Campo A, Gu ́ery-Odelin D, Ruschhaupt A, Chen X and Muga J G 2013 Shortcuts to adiabaticity Advances in atomic, molecular, and optical physics vol 62 (Elsevier) pp 117–169
[186] Hartmann A and Lechner W 2018 arXiv preprint arXiv:1807.02053
[187] Oliver W D and Welander P B 2013 MRS Bulletin 38 816
[188] Paik H, Schuster D, Bishop L S, Kirchmair G, Catelani G, Sears A, Johnson B, Reagor M, Frunzio L, Glazman L et al. 2011 Physical Review Letters 107 240501
[189] Rigetti C, Gambetta J M, Poletto S, Plourde B L T, Chow J M, C ́orcoles A D, Smolin J A, Merkel S T, Rozen J R, Keefe G A, Rothwell M B, Ketchen M B and Steffen M 2012 Phys. Rev. B 86 100506 URL https://link.aps.org/doi/10.1103/PhysRevB.86.100506
[190] Jin X Y, Kamal A, Sears A P, Gudmundsen T, Hover D, Miloshi J, Slattery R, Yan F, Yoder J, Orlando T P, Gustavsson S and Oliver W D 2015 Phys. Rev. Lett. 114 240501 URL https://link.aps.org/doi/10.1103/PhysRevLett.114.240501
[191] Yan F, Campbell D, Krantz P, Kjaergaard M, Kim D, Yoder J L, Hover D, Sears A, Kerman A J, Orlando T P, Gustavsson S and Oliver W D 2018 Phys. Rev. Lett. 120 260504 URL https://link.aps.org/doi/10.1103/PhysRevLett.120.260504
[192] Orlando T, Mooij J, Tian L, van der Wal C H, Levitov L, Lloyd S and Mazo J 1999 Phys. Rev. B 60 15398–15413
[193] Mooij J, Orlando T, Levitov L, Tian L, van der Wal C H and Lloyd S 1999 Science 285 1036–1039 [194] Harris R, Berkley A, Johnson M, Bunyk P, Govorkov S, Thom M, Uchaikin S, Wilson A, Chung J, Holtham E, Biamonte J, Smirnov A, Amin M and Massen van den Brink A 2007 Phys. Rev. Lett. 98 177001
[195] Kerman A 209 in preparation
[196] Macklin C, O’Brien K, Hover D, Schwartz M, Bolkhovsky V, Zhang X, Oliver W and Siddiqi I 2015 Science 350 307
[197] Tolpygo S, Bolkhovsky V, Weir T, Johnson L, Gouker M and Oliver W 2014 IEEE Trans. Appl. Supercond. 25 1101312
[198] Jurcevic P, Lanyon B P, Hauke P, Hempel C, Zoller P, Blatt R and Roos C F 2014 Nature 511 202
[199] Smith J, Lee A, Richerme P, Neyenhuis B, Hess P W, Hauke P, Heyl M, Huse D and Monroe C 2016 Nature Physics 12 907911
[200] Maier C, Brydges T, Jurcevic P, Trautmann N, Hempel C, Lanyon B P, Hauke P, Blatt R and Roos C F 2019 Phys. Rev. Lett. 122 050501
[201] Cirac J I and Zoller P 1995 Physical review letters 74 4091
[202] Sørensen A and Mølmer K 1999 Phys. Rev. Lett. 83 2274
[203] Mintert F and Wunderlich C 2001 Phys. Rev. Lett. 87 257904
[204] Britton J W, Sawyer B C, Keith A C, Wang C C J, Freericks J K, Uys H, Biercuk M J and Bollinger J J 2012 Nature 484 489
[205] Islam R, Senko C, Campbell W C, Korenblit S, Smith J, Lee A, Edwards E E, Wang C C J, Freericks J K and Monroe C 2013 Science 340 583
[206] Richerme P, Senko C, Smith J, Lee A, Korenblit S and Monroe C 2013 Phys. Rev. A 88 012334 [207] Nevado P and Porras D 2016 Phys. Rev. A 93 013625
[208] Nils Trautmann P H 2018 Phys. Rev. A 97 023606
[209] Friedenauer A, Schmitz H, Glueckert J T, Porras D and Schaetz T 2008 Nat. Phys. 4 757
[210] Graß T, Ravent ́os D, Juli ́a-D ́ıaz B, Gogolin C and Lewenstein M 2016 Nature communications 7 11524
[211] Korenblit S, Kafri D, Campbell W C, Islam R, Edwards E E, Gong Z X, Lin G D, Duan L M, Kim J, Kim K and Monroe C 2012 New J. Phys. 14 095024
[212] Zhang J, Pagano G, Hess P, Kyprianidis A, Becker P, Kaplan H, Gorshkov A, Gong Z X and Monroe C 2017 Nature 551 601604
[213] Friis N, Marty O, Maier C, Hempel C, Holzpfel M, Jurcevic P, Plenio M B, Huber M, Roos C, Blatt R and Lanyon B 2018 Phys. Rev. X 8 021012
[214] Pagano G, Hess P, Kaplan H B, Tan W L, Richerme P, Becker P, Kyprianidis A, Zhang Jand Birckelbaw E, Hernandez M Rand Wu Y and Monroe C 2018 Quantum Science and Technology 4
[215] Safavi-Naini A, Lewis-Swan R J, Bohnet J G, Garttner M, Gilmore K A, Jordan J E, Cohn J, Freericks J K, Rey A M and Bollinger J J 2018 Phys. Rev. Lett. 121 040503
[216] Zippilli S, Johanning M, Giampaolo S M, Wunderlich C and Illuminati F 2014 Phys. Rev. A 89 042308
[217] Seidelin S, Chiaverini J, Reichle R, Bollinger J J, Leibfried D, Britton J, Wesenberg J H and Blakestad R B 2006 Phys. Rev. Lett. 96 253003
[218] Schmied R, Wesenberg J H and Leibfried D 2009 Phys. Rev. Lett. 102 233002
[219] Hakelberg F, Kiefer P, Wittemer M, Warring U and Schaetz T 2018 arXiv preprint arXiv:1812.08552
[220] Ivan A Boldin Alexander Kraft C W 2018 Phys. Rev. Lett. 120 023201
[221] Soare A, Ball H, Hayes D, Zhen X, Jarratt M C, Sastrawan J, Uys H and Biercuk M J 2014 Phys. Rev. A 89 042329
[222] Gorman D J, Hemmerling B, Megidish E, Moeller S A, Schindler P, Sarovar M and Haeffner H 2018 Phys. Rev. X 8 011038
[223] Saffman M 2016 ArXiv e-prints
[224] Jaksch D, Cirac J, Zoller P, Rolston S, Cˆot ́e R and Lukin M 2000 Physical Review Letters 85 2208
[225] Schauß P, Zeiher J, Fukuhara T, Hild S, Cheneau M, Macr`ı T, Pohl T, Bloch I and Gross C 2015 Science 347 1455–1458 ISSN 0036-8075 URL http://science.sciencemag.org/content/347/6229/1455
[226] Maller K M, Lichtman M T, Xia T, Sun Y, Piotrowicz M J, Carr A W, Isenhower L and Saffman M 2015 Phys. Rev. A 92 022336 URL http://link.aps.org/doi/10.1103/PhysRevA.92. 022336
[227] Jau Y Y, Hankin A, Keating T, Deutsch I and Biedermann G 2016 Nature Physics 12 71
[228] Labuhn H, Barredo D, Ravets S, de Leseleuc S, Macri T, Lahaye T and Browaeys A 2016 Nature, 534 667–670
[229] Pichler H, Wang S T, Zhou L, Choi S and Lukin M D 2018 arXiv preprint arXiv:1808.10816 [230] Torggler V, Aumann P, Ritsch H and Lechner W 2018 arXiv preprint arXiv:1803.00735
[231] Landig R, Hruby L, Dogra N, Landini M, Mottl R, Donner T and Esslinger T 2016 Nature 532

2

Quantum annealing of the p-spin model under inhomogeneous transverse field driving
Authors: Yuki Susa, Yu Yamashiro, Masayuki Yamamoto, Itay Hen, Daniel A. Lidar, Hidetoshi Nishimori
https://arxiv.org/abs/1808.01582
(Submitted on 5 Aug 2018 (v1), last revised 21 Oct 2018 (this version, v2))
Phys. Rev. A 98, 042326 (2018)

[1] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[2] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and
D. Preda, Science 292, 472 (2001).
[3] G. E. Santoro, R. Martoňák, E. Tosatti, and R. Car, Science
295, 2427 (2002).
[4] G. E. Santoro and E. Tosatti, J. Phys. A 39, R393 (2006).
[5] A. Das and B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
[6] S. Morita and H. Nishimori, J. Math. Phys. 49, 125210 (2008).
[7] T. Albash and D. A. Lidar, Rev. Mod. Phys. 90, 015002 (2018).
[8] A. Lucas, Front. Phys. 2, 5 (2014).
[9] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220,
671 (1983).
[10] S. Jansen, M.-B. Ruskai, and R. Seiler, J. Math. Phys. 48,
102111 (2007).
[11] D. A. Lidar, A. T. Rezakhani, and A. Hamma, J. Math. Phys.
50, 102106 (2009).
[12] C. R. Laumann, R. Moessner, A. Scardicchio, and S. L. Sondhi,
Phys. Rev. Lett. 109, 030502 (2012).
[13] J. Tsuda, Y. Yamanaka, and H. Nishimori, J. Phys. Soc. Jpn. 82,
114004 (2013).
[14] H. Nishimori and G. Ortiz, Elements of Phase Transitions and
Critical Phenomena (Oxford University Press, Oxford, U.K.,
2011).
[15] J. E. Avron, M. Fraas, G. M. Graf, and P. Grech, Commun.
Math. Phys. 314, 163 (2012).
[16] L. C. Venuti, T. Albash, D. A. Lidar, and P. Zanardi, Phys. Rev.
A 93, 032118 (2016).
[17] L. C. Venuti, T. Albash, M. Marvian, D. Lidar, and P. Zanardi,
Phys. Rev. A 95, 042302 (2017).
[18] T. Jörg, F. Krzakala, J. Kurchan, and A. C. Maggs, Phys. Rev.
Lett. 101, 147204 (2008).
[19] T. Jörg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pujos,
Europhys. Lett. 89, 40004 (2010).
[20] H. Nishimori, J. Tsuda, and S. Knysh, Phys. Rev. E 91, 012104
(2015).
[21] S. Matsuura, H. Nishimori, T. Albash, and D. A. Lidar, Phys.
Rev. Lett. 116, 220501 (2016).
[22] S. Matsuura, H. Nishimori, W. Vinci, T. Albash, and D. A.
Lidar, Phys. Rev. A 95, 022308 (2017).
[23] C. R. Laumann, R. Moessner, A. Scardicchio, and S. L. Sondhi,
Eur. Phys. J. Spec. Top. 224, 75 (2015).
[24] G. A. Durkin, arXiv:1806.07602.
[25] Y. Seki and H. Nishimori, Phys. Rev. E 85, 051112 (2012).
[26] B. Seoane and H. Nishimori, J. Phys. A 45, 435301 (2012).
[27] Y. Seki and H. Nishimori, J. Phys. A 48, 335301 (2015).
[28] H. Nishimori and K. Takada, Front. ICT 4, 2 (2017).
[29] M. Ohkuwa, H. Nishimori, and D. A. Lidar, Phys. Rev. A 98,
022314 (2018).
for the case (c) a discontinuity exists at the transition point, a feature of a first-order phase transition [55].
[30] M. M. Rams, M. Mohseni, and A. del Campo, New J. Phys. 18, 123034 (2016).
[31] M. Mohseni, J. Strumpfer, and M. M. Rams, arXiv:1804.11037. [32] J. Dziarmaga and M. M. Rams, New J. Phys. 12, 055007 (2010). [33] W. H. Zurek and U. Dorner, Philos. Trans. R. Soc., A 366, 2953
(2008).
[34] E. Farhi, J. Goldstone, D. Gosset, S. Gutmann, H. B. Meyer,
and P. Shor, Quantum Inf. Process. 11, 181 (2011).
[35] N. G. Dickson and M. H. S. Amin, Phys. Rev. Lett. 106, 050502
(2011).
[36] N. G. Dickson and M. H. Amin, Phys. Rev. A 85, 032303 (2012). [37] T. Lanting, A. D. King, B. Evert, and E. Hoskinson, Phys. Rev.
A 96, 042322 (2017).
[38] A. Del Campo, T. W. B. Kibble, and W. Zurek, J. Phys.: Con-
dens. Matter 25, 404210 (2013).
[39] F. Gómez-Ruiz and A. del Campo, arXiv:1805.00525.
[40] J. I. Adame and P. L. McMahon, arXiv:1806.11091.
[41] M. Okuyama and M. Ohzeki, arXiv:1808.09707.
[42] Y. Susa, Y. Yamashiro, M. Yamamoto, and H. Nishimori, J.
Phys. Soc. Jpn. 87, 023002 (2018).
[43] L. K. Grover, Phys. Rev. Lett. 79, 325 (1997).
[44] M. Filippone, S. Dusuel, and J. Vidal, Phys. Rev. A 83, 022327
(2011).
[45] T. Ichikawa, Master’s thesis, Tokyo Institute of Technology,
2014.
[46] S. Shin, G. Smith, A. Smolin, and U. Vaziriani,
arXiv:1404.6499.
[47] T. F. Rønnow, Z. Wang, J. Job, S. Boixo, S. V. Isakov, D. Wecker,
J. M. Martinis, D. A. Lidar, and M. Troyer, Science 345, 420
(2014).
[48] T. Albash, T. F. Rønnow, M. Troyer, and D. A. Lidar, Eur. Phys.
J. Spec. Top. 224, 111 (2015).
[49] T. Albash, W. Vinci, A. Mishra, P. A. Warburton, and D. A.
Lidar, Phys. Rev. A 91, 042314 (2015).
[50] K. L. Pudenz, T. Albash, and D. A. Lidar, Phys. Rev. A 91,
042302 (2015).
[51] S. Boixo, V. N. Smelyanskiy, A. Shabani, S. V. Isakov, M. Dyk-
man, V. S. Denchev, M. H. Amin, A. Y. Smirnov, M. Mohseni,
and H. Neven, Nat. Commun. 7, 10327 (2016).
[52] A. Mishra, T. Albash, and D. A. Lidar, Nat. Commun. 9, 2917
(2018).
[53] P. J. D. Crowley, T. Durić, W. Vinci, P. A. Warburton, and A. G.
Green, Phys. Rev. A 90, 042317 (2014).
[54] A. del Campo and W. H. Zurek, Int. J. Mod. Phys. A 29, 1430018
(2014).
[55] L. A. Wu, M. S. Sarandy, and D. A. Lidar, Phys. Rev. Lett. 93,
250404 (2004).

3

Reverse annealing for the fully connected p-spin model
Authors: Masaki Ohkuwa, Hidetoshi Nishimori, Daniel A. Lidar
https://arxiv.org/abs/1806.02542
(Submitted on 7 Jun 2018)
Phys. Rev. A 98, 022314 (2018)

[1] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[2] J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli, Science 284, 779 (1999).
[3] G. E. Santoro, R. Martona ́k, E. Tosatti, and R. Car, Science 295, 2427 (2002).
[4] G. E. Santoro and E. Tosatti, J. Phys. A: Math. Gen. 39, R393 (2006).
[5] A. Das and B. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
[6] S. Morita and H. Nishimori, J. Math. Phys. 49, 125210 (2008).
[7] S. Tanaka, R. Tamura, and B. K. Chakrabarti, Quantum Spin Glasses, Annealing, and Computation
(Cambridge University Press, 2017).
[8] E. Farhi, J. Goldstone, S. Gutmann, and S. Michael, arXiv:0001106 (2000).
[9] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science 292, 472 (2001).
[10] T. Albash and D. A. Lidar, Rev. Mod. Phys. 90, 015002 (2018).
[11] A. Lucas, Frontiers in Phys. 2, 1 (2014).
[12] A. Perdomo-Ortiz, S. E. Venegas-Andraca, and A. Aspuru-Guzik, Quantum Information Processing
10, 33 (2011).
[13] A.D.King,J.Carrasquilla,I.Ozfidan,J.Raymond,E.Andriyash,A.Berkley,M.Reis,T.M.Lanting,
R. Harris, G. Poulin-Lamarre, A. Y. Smirnov, C. Rich, F. Altomare, P. Bunyk, J. Whittaker, L. Swen- son, E. Hoskinson, Y. Sato, M. Volkmann, E. Ladizinsky, M. Johnson, J. Hilton, and M. H. Amin, arXiv:1803.02047 (2018).
[14] T. Jo ̈rg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pujos, EPL 89, 40004 (2010).
[15] Y. Seki and H. Nishimori, Phy. Rev. E 85, 051112 (2012).
[16] Manaka Okuyama (private communication) recently proved that the static approximation gives the
exact solution in the present problem. We nevertheless use the term ‘static approximation’ following
the convention.
[17] S. Bravyi, D. P. Di Vincenzo, R. Oliveira, and B. M. Terhal, Quanum Inf. Comput. 8, 361 (2008).
[18] B. Seoane and H. Nishimori, J. Phys. A: Math. Theor. 45, 435301 (2012).
[19] H. Nishimori and K. Takada, Frontiers in ICT 4, 2 (2017).
[20] M. Marvian, D. A. Lidar, and I. Hen, arXiv:1802.03408 (2018).
[21] S. W. Shin, G. Smith, J. A. Smolin, and U. Vazilani, arXiv:1401.7087 (2014).
[22] Y. Susa, J. F. Jadebeck, and H. Nishimori, Physical Review A 95, 042321 (2017).

4

Nested Quantum Annealing Correction at Finite Temperature: p-spin models
Authors: Shunji Matsuura, Hidetoshi Nishimori, Walter Vinci, Daniel A. Lidar
https://arxiv.org/abs/1803.01492
(Submitted on 5 Mar 2018)
Phys. Rev. A. 99, 062307 (2019)

[1] A. B. Finnila, M. A. Gomez, C. Sebenik, C. Stenson, and J. D. Doll, “Quantum annealing: A new method for min- imizing multidimensional functions,” Chemical Physics Letters 219, 343–348 (1994).
[2] Tadashi Kadowaki and Hidetoshi Nishimori, “Quantum annealing in the transverse Ising model,” Phys. Rev. E 58, 5355 (1998).
[3] Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Joshua Lapan, Andrew Lundgren, and Daniel Preda, “A quan- tum adiabatic evolution algorithm applied to random in- stances of an np-complete problem,” Science 292, 472 (2001).
[4] J. Brooke, D. Bitko, T. F., Rosenbaum, and G. Aeppli, “Quantum annealing of a disordered magnet,” Science 284, 779–781 (1999).
[5] J. Brooke, T. F. Rosenbaum, and G. Aeppli, “Tunable quantum tunnelling of magnetic domain walls,” Nature 413, 610–613 (2001).
[6] GiuseppeE.Santoro,RomanMartonˇa ́k,ErioTosatti, and Roberto Car, “Theory of quantum annealing of an Ising spin glass,” Science 295, 2427–2430 (2002).
[7] Arnab Das and Bikas K. Chakrabarti, “Colloquium: Quantum annealing and analog quantum computation,” Rev. Mod. Phys. 80, 1061–1081 (2008).
[8] W. M. Kaminsky and S. Lloyd, “Scalable Architecture for Adiabatic Quantum Computing of NP-Hard Problems,” in Quantum Computing and Quantum Bits in Mesoscopic Systems, edited by A.A.J. Leggett, B. Ruggiero, and P. Silvestrini (Kluwer Academic/Plenum Publ., 2004) arXiv:quant-ph/0211152.
[9] William M. Kaminsky, Seth Lloyd, and Terry P. Or- lando, “Quantum computing and quantum bits in meso-
exponents. The coefficients in these equations, 2JCλ and √4JCλ, would be the leading terms of asymptotic expansions of the relevant coefficient g(C) in the limit of C ≫ 1. In other words, it is expected that the gap closes as g(C)􏰗|Γ − Γc| for general values of C with g(C) having the above asymptotic forms for C ≫ 1.
scopic systems,” (Springer, New York, 2004) Chap. 25,
pp. 229–236.
[10] R. Harris, J. Johansson, A. J. Berkley, M. W. Johnson,
T. Lanting, Siyuan Han, P. Bunyk, E. Ladizinsky, T. Oh, I. Perminov, E. Tolkacheva, S. Uchaikin, E. M. Chapple, C. Enderud, C. Rich, M. Thom, J. Wang, B. Wilson, and G. Rose, “Experimental demonstration of a robust and scalable flux qubit,” Phys. Rev. B 81, 134510 (2010).
[11] R. Harris, M. W. Johnson, T. Lanting, A. J. Berkley, J. Johansson, P. Bunyk, E. Tolkacheva, E. Ladizinsky, N. Ladizinsky, T. Oh, F. Cioata, I. Perminov, P. Spear, C. Enderud, C. Rich, S. Uchaikin, M. C. Thom, E. M. Chapple, J. Wang, B. Wilson, M. H. S. Amin, N. Dickson, K. Karimi, B. Macready, C. J. S. Truncik, and G. Rose, “Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor,” Phys. Rev. B 82, 024511 (2010).
[12] A J Berkley, M W Johnson, P Bunyk, R Harris, J Johansson, T Lanting, E Ladizinsky, E Tolkacheva, M H S Amin, and G Rose, “A scalable readout sys- tem for a superconducting adiabatic quantum optimiza- tion system,” Superconductor Science and Technology 23, 105014 (2010).
[13] M. W. Johnson, M. H. S. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, A. J. Berkley, J. Jo- hansson, P. Bunyk, E. M. Chapple, C. Enderud, J. P. Hilton, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, C. J. S. Truncik, S. Uchaikin, J. Wang, B. Wilson, and G. Rose, “Quantum annealing with manufactured spins,” Nature 473, 194–198 (2011).
[14] A. J. Berkley, A. J. Przybysz, T. Lanting, R. Harris,
N. Dickson, F. Altomare, M. H. Amin, P. Bunyk, C. En- derud, E. Hoskinson, M. W. Johnson, E. Ladizinsky, R. Neufeld, C. Rich, A. Yu. Smirnov, E. Tolkacheva, S. Uchaikin, and A. B. Wilson, “Tunneling spectroscopy using a probe qubit,” Phys. Rev. B 87, 020502– (2013).
[15] P. I Bunyk, E. M. Hoskinson, M. W. Johnson, E. Tolka- cheva, F. Altomare, AJ. Berkley, R. Harris, J. P. Hilton, T. Lanting, AJ. Przybysz, and J. Whittaker, “Archi- tectural considerations in the design of a superconduct- ing quantum annealing processor,” IEEE Transactions on Applied Superconductivity 24, 1–10 (Aug. 2014).
[16] T. Lanting, A. J. Przybysz, A. Yu. Smirnov, F. M. Spedalieri, M. H. Amin, A. J. Berkley, R. Harris, F. Al- tomare, S. Boixo, P. Bunyk, N. Dickson, C. Enderud, J. P. Hilton, E. Hoskinson, M. W. Johnson, E. Ladizin- sky, N. Ladizinsky, R. Neufeld, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, S. Uchaikin, A. B. Wilson, and G. Rose, “Entanglement in a quantum an- nealing processor,” Phys. Rev. X 4, 021041– (2014).
[17] N. G. Dickson, M. W. Johnson, M. H. Amin, R. Harris, F. Altomare, A. J. Berkley, P. Bunyk, J. Cai, E. M. Chap- ple, P. Chavez, F. Cioata, T. Cirip, P. deBuen, M. Drew- Brook, C. Enderud, S. Gildert, F. Hamze, J. P. Hilton, E. Hoskinson, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Lanting, T. Mahon, R. Neufeld, T. Oh, I. Perminov, C. Petroff, A. Przybysz, C. Rich, P. Spear, A. Tcaciuc, M. C. Thom, E. Tolkacheva, S. Uchaikin, J. Wang, A. B. Wilson, Z. Merali, and G. Rose, “Thermally assisted quantum annealing of a 16-qubit problem,” Nat. Com- mun. 4, 1903 (2013).
[18] Sergio Boixo, Tameem Albash, Federico M. Spedalieri, Nicholas Chancellor, and Daniel A. Lidar, “Experimen- tal signature of programmable quantum annealing,” Nat. Commun. 4, 2067 (2013).
[19] Sergio Boixo, Troels F. Ronnow, Sergei V. Isakov, Zhihui Wang, David Wecker, Daniel A. Lidar, John M. Martinis, and Matthias Troyer, “Evidence for quantum annealing with more than one hundred qubits,” Nat. Phys. 10, 218– 224 (2014).
[20] T. Albash, T. F. Rønnow, M. Troyer, and D. A. Lidar, “Reexamining classical and quantum models for the D- Wave One processor,” Eur. Phys. J. Spec. Top. 224, 111– 129 (2015).
[21] Tameem Albash, Itay Hen, Federico M. Spedalieri, and Daniel A. Lidar, “Reexamination of the evidence for en- tanglement in a quantum annealer,” Physical Review A 92, 062328– (2015).
[22] John A. Smolin and Graeme Smith, “Classical signature of quantum annealing,” Frontiers in Physics 2, 52 (2014).
[23] Lei Wang, Troels F. Rønnow, Sergio Boixo, Sergei V. Isakov, Zhihui Wang, David Wecker, Daniel A. Li- dar, John M. Martinis, and Matthias Troyer, “Com- ment on: ‘Classical signature of quantum annealing’,”
arXiv:1305.5837 (2013).
[24] Seung Woo Shin, Graeme Smith, John A. Smolin, and
Umesh Vazirani, “How “quantum” is the D-Wave ma-
chine?” arXiv:1401.7087 (2014).
[25] Seung Woo Shin, Graeme Smith, John A. Smolin, and
Umesh Vazirani, “Comment on ”distinguishing clas- sical and quantum models for the D-Wave device”,” arXiv:1404.6499 (2014).
[26] Troels F. Rønnow, Zhihui Wang, Joshua Job, Sergio Boixo, Sergei V. Isakov, David Wecker, John M. Mar- tinis, Daniel A. Lidar, and Matthias Troyer, “Defining
and detecting quantum speedup,” Science 345, 420–424
(2014).
[27] Sergio Boixo, Vadim N. Smelyanskiy, Alireza Shabani,
Sergei V. Isakov, Mark Dykman, Vasil S. Denchev, Mohammad H. Amin, Anatoly Yu Smirnov, Masoud Mohseni, and Hartmut Neven, “Computational multi- qubit tunnelling in programmable quantum annealers,” Nat Commun 7 (2016).
[28] Davide Venturelli, Salvatore Mandra, Sergey Knysh, Bryan O’Gorman, Rupak Biswas, and Vadim Smelyan- skiy, “Quantum optimization of fully connected spin glasses,” Phys. Rev. X 5, 031040– (2015). [29] James King, Sheir Yarkoni, Jack Raymond, Isil Ozfi- dan, Andrew D. King, Mayssam Mohammadi Nevisi, Jeremy P. Hilton, and Catherine C. McGeoch, “Quan- tum annealing amid local ruggedness and global frustra- tion,” arXiv:1701.04579 (2017). [30] Catherine C. McGeoch and Cong Wang, “Experimental evaluation of an adiabatic quantum system for combi- natorial optimization,” in Proceedings of the 2013 ACM Conference on Computing Frontiers (2013). [31] James King, Sheir Yarkoni, Mayssam M. Nevisi, Jeremy P. Hilton, and Catherine C. McGeoch, “Bench- marking a quantum annealing processor with the time- to-target metric,” arXiv:1508.05087 (2015). [32] Itay Hen, Joshua Job, Tameem Albash, Troels F. Rønnow, Matthias Troyer, and Daniel A. Lidar, “Prob- ing for quantum speedup in spin-glass problems with planted solutions,” Phys. Rev. A 92, 042325 (2015). [33] Helmut G. Katzgraber, Firas Hamze, Zheng Zhu, An- drew J. Ochoa, and H. Munoz-Bauza, “Seeking quan- tum speedup through spin glasses: The good, the bad, and the ugly,” Phys. Rev. X 5, 031026– (2015). [34] Vasil S. Denchev, Sergio Boixo, Sergei V. Isakov, Nan Ding, Ryan Babbush, Vadim Smelyanskiy, John Marti- nis, and Hartmut Neven, “What is the computational value of finite-range tunneling?” Phys. Rev. X 6, 031015 (2016). [35] Salvatore Mandra, Zheng Zhu, Wenlong Wang, Alejandro Perdomo-Ortiz, and Helmut G. Katzgraber, “Strengths and weaknesses of weak-strong cluster problems: A detailed overview of state-of-the-art classical heuristics versus quantum approaches,” Physical Review A 94, 022337– (2016).
[36] Walter Vinci and Daniel A. Lidar, “Optimally stopped optimization,” Physical Review Applied 6, 054016– (2016).
[37] Tameem Albash and Daniel A. Lidar, “Evidence for a limited quantum speedup on a quantum annealer,” arXiv:1705.07452 (2017).
[38] Salvatore Mandr`a and Helmut G. Katzgraber, “A deceptive step towards quantum speedup detection,” arXiv:1711.01368 (2017).
[39] Fei Yan, Simon Gustavsson, Archana Kamal, Jeffrey Birenbaum, Adam P Sears, David Hover, Ted J. Gud- mundsen, Danna Rosenberg, Gabriel Samach, S Weber, Jonilyn L. Yoder, Terry P. Orlando, John Clarke, An- drew J. Kerman, and William D. Oliver, “The flux qubit revisited to enhance coherence and reproducibility,” Na- ture Communications 7, 12964 EP – (2016).
[40] Steven J. Weber, Gabriel O. Samach, David Hover, Si- mon Gustavsson, David K. Kim, Alexander Melville, Danna Rosenberg, Adam P. Sears, Fei Yan, Jonilyn L. Yoder, William D. Oliver, and Andrew J. Kerman, “Coherent coupled qubits for quantum annealing,” Physical
Review Applied 8, 014004– (2017).
[41] R. Islam, C. Senko, W. C. Campbell, S. Korenblit,
J. Smith, A. Lee, E. E. Edwards, C. C. J. Wang, J. K. Freericks, and C. Monroe, “Emergence and frustration of magnetism with variable-range interactions in a quan- tum simulator,” Science 340, 583–587 (2013).
[42] J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, “Many-body localization in a quantum simulator with programmable random disorder,” Nature Physics 12, 907 EP – (2016).
[43] Jonathan Simon, Waseem S. Bakr, Ruichao Ma, M. Eric Tai, Philipp M. Preiss, and Markus Greiner, “Quantum simulation of antiferromagnetic spin chains in an optical lattice,” Nature 472, 307 EP – (2011).
[44] Martin Boll, Timon A. Hilker, Guillaume Salomon, Ahmed Omran, Jacopo Nespolo, Lode Pollet, Immanuel Bloch, and Christian Gross, “Spin- and density-resolved microscopy of antiferromagnetic correlations in fermi- hubbard chains,” Science 353, 1257 (2016).
[45] Hendrik Weimer, Markus Mu ̈ller, Igor Lesanovsky, Peter Zoller, and Hans Peter Bu ̈chler, “A rydberg quantum simulator,” Nature Physics 6, 382 EP – (2010).
[46] Thanh Long Nguyen, Jean-Michel Raimond, Cl ́ement Sayrin, Rodrigo Cortinas, Tigrane Cantat-Moltrecht, F ́ed ́eric Assemat, Igor Dotsenko, S ́ebastien Gleyzes, Serge Haroche, Guillaume Roux, Thierry Jolicoeur, and Michel Brune, “Towards quantum simulation with circu- lar rydberg atoms,” arXiv:1707.04397 (2017).
[47] Hannes Bernien, Sylvain Schwartz, Alexander Keesling, Harry Levine, Ahmed Omran, Hannes Pichler, Soon- won Choi, Alexander S. Zibrov, Manuel Endres, Markus Greiner, Vladan Vuleti ́c, and Mikhail D. Lukin, “Prob- ing many-body dynamics on a 51-atom quantum simula- tor,” arXiv:1707.04344 (2017).
[48] J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z. X. Gong, and C. Monroe, “Observation of a many-body dynami- cal phase transition with a 53-qubit quantum simulator,” arXiv:1708.01044 (2017).
[49] Richard P. Feynman, “Quantum mechanical computers,” Optics News, Optics News 11, 11–20 (1985).
[50] R.P. Feynman, “Simulating Physics with Computers,” Intl. J. Theor. Phys. 21, 467 (1982).
[51] D. Deutsch and R. Jozsa, “Rapid Solution of Problems by Quantum Computation,” Proc. R. Soc. London Ser. A 439, 553 (1992).
[52] E. Bernstein and U. Vazirani, “Quantum Complexity Theory,” in Proceedings of the 25th Annual ACM Sym- posium on Theory of Computing (ACM, New York, NY, 1993) p. 11.
[53] P. W. Shor, “Algorithms for quantum computation: dis- crete logarithms and factoring,” Foundations of Com- puter Science, 1994 Proceedings., 35th Annual Sympo- sium on, 35th Annual Symposium on Foundations of Computer Science, 1994 Proceedings , 124–134 (20-22 Nov 1994).
[54] Lov K. Grover, “A fast quantum mechanical algorithm for database search,” in Proceedings of the Twenty- eighth Annual ACM Symposium on Theory of Comput- ing, STOC ’96 (ACM, New York, NY, USA, 1996) pp. 212–219.
[55] Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and
Michael Sipser, “Quantum Computation by Adiabatic
Evolution,” arXiv:quant-ph/0001106 (2000).
[56] M. Born and V. Fock, “Beweis des adiabatensatzes,”
Zeitschrift fu ̈r Physik 51, 165 (1928).
[57] T. Kato, “On the adiabatic theorem of quantum mechan-
ics,” J. Phys. Soc. Jap. 5, 435 (1950).
[58] L. M. Garrido and F. J. Sancho, “Degree of approximate
validity of the adiabatic invariance in quantum mechan-
ics,” Physica 28, 553–560 (1962).
[59] G. Nenciu, “On the adiabatic theorem of quantum me-
chanics,” J. Phys. A: Math. Gen. 13, L15 (1980).
[60] J. E. Avron, R. Seiler, and L. G. Yaffe, “Adiabatic theo- rems and applications to the quantum hall effect,” Com- mun. Math. Phys. 110, 33–49 (1987), erratum: ibid, 156,
649 (1993).
[61] George A. Hagedorn and Alain Joye, “Elementary expo-
nential error estimates for the adiabatic approximation,”
J. Math. Anal. Appl. 267, 235–246 (2002).
[62] Sabine Jansen, Mary-Beth Ruskai, and Ruedi Seiler, “Bounds for the adiabatic approximation with appli- cations to quantum computation,” J. Math. Phys. 48,
102111 (2007).
[63] Daniel A. Lidar, Ali T. Rezakhani, and Alioscia Hamma,
“Adiabatic approximation with exponential accuracy for many-body systems and quantum computation,” J. Math. Phys. 50, 102106 (2009).
[64] Yimin Ge, Andra ́s Molna ́r, and J. Ignacio Cirac, “Rapid adiabatic preparation of injective pro jected entangled pair states and gibbs states,” Physical Review Letters 116, 080503– (2016).
[65] S. Bachmann, W. De Roeck, and M. Fraas, “Adiabatic theorem for quantum spin systems,” Physical Review Letters 119, 060201– (2017).
[66] Tameem Albash and Daniel A. Lidar, “Adiabatic quan- tum computing,” Rev. Mod. Phys. (accepted) (2016).
[67] S. P. Jordan, E. Farhi, and P. W. Shor, “Error-correcting codes for adiabatic quantum computation,” Phys. Rev. A 74, 052322 (2006).
[68] G. Quiroz and D. A. Lidar, “High-fidelity adiabatic quan- tum computation via dynamical decoupling,” Phys. Rev. A 86, 042333 (2012).
[69] Kevin C. Young, Mohan Sarovar, and Robin Blume- Kohout, “Error suppression and error correction in adi- abatic quantum computation: Techniques and chal- lenges,” Phys. Rev. X 3, 041013– (2013).
[70] Mohan Sarovar and Kevin C Young, “Error suppression and error correction in adiabatic quantum computation: non-equilibrium dynamics,” New J. of Phys. 15, 125032 (2013).
[71] Kevin C. Young, Robin Blume-Kohout, and Daniel A. Lidar, “Adiabatic quantum optimization with the wrong hamiltonian,” Phys. Rev. A 88, 062314– (2013).
[72] Adam D. Bookatz, Edward Farhi, and Leo Zhou, “Error suppression in hamiltonian-based quantum computation using energy penalties,” Physical Review A 92, 022317– (2015).
[73] Iman Marvian and Daniel A. Lidar, “Quantum error sup- pression with commuting hamiltonians: Two local is too local,” Phys. Rev. Lett. 113, 260504– (2014).
[74] Zhang Jiang and Eleanor G. Rieffel, “Non-commuting two-local hamiltonians for quantum error suppression,” Quantum Information Processing 16, 89 (2017).
[75] Iman Marvian, “Exponential suppression of decoher- ence and relaxation of quantum systems using energy
penalty,” arXiv:1602.03251 (2016).
[76] Milad Marvian and Daniel A. Lidar, “Error Suppres-
sion for Hamiltonian-Based Quantum Computation Us- ing Subsystem Codes,” Physical Review Letters 118, 030504– (2017).
[77] D. A. Lidar, “Towards fault tolerant adiabatic quantum computation,” Phys. Rev. Lett. 100, 160506 (2008).
[78] Anand Ganti, Uzoma Onunkwo, and Kevin Young,
“Family of [[6k,2k,2]] codes for practical, scalable adia- batic quantum computation,” Phys. Rev. A 89, 042313– (2014).
[79] Kristen L Pudenz, Tameem Albash, and Daniel A Li- dar, “Error-corrected quantum annealing with hundreds of qubits,” Nat. Commun. 5, 3243 (2014).
[80] Kristen L. Pudenz, Tameem Albash, and Daniel A. Li- dar, “Quantum annealing correction for random Ising problems,” Phys. Rev. A 91, 042302 (2015).
[81] Anurag Mishra, Tameem Albash, and Daniel A. Lidar, “Performance of two different quantum annealing correc- tion codes,” Quant. Inf. Proc. 15, 609–636 (2015).
[82] Walter Vinci, Tameem Albash, Gerardo Paz-Silva, Itay Hen, and Daniel A. Lidar, “Quantum annealing correc- tion with minor embedding,” Phys. Rev. A 92, 042310– (2015).
[83] Walter Vinci, Tameem Albash, and Daniel A Lidar, “Nested quantum annealing correction,” Nature Quan- tum Information 2, 16017 (2016).
[84] Walter Vinci and Daniel A. Lidar, “Scalable effec- tive temperature reduction for quantum annealers via nested quantum annealing correction,” arXiv:1710.07871 (2017).
[85] Shunji Matsuura, Hidetoshi Nishimori, Tameem Albash,
and Daniel A. Lidar, “Mean field analysis of quan- tum annealing correction,” Physical Review Letters 116, 220501– (2016).
[86] Shunji Matsuura, Hidetoshi Nishimori, Walter Vinci, Tameem Albash, and Daniel A. Lidar, “Quantum- annealing correction at finite temperature: Ferromag- netic p-spin models,” Physical Review A 95, 022308 (2017).
[87] A. Lucas, “Ising formulations of many NP problems,” Front. Phys. 2, 5 (2014).
[88] Masuo Suzuki, “Relationship between d-dimensional quantal spin systems and (d+1)-dimensional ising sys- tems: Equivalence, critical exponents and systematic ap- proximants of the partition function and spin correla- tions,” Progress of Theoretical Physics 56, 1454–1469 (1976).
[89] B Seoane and H Nishimori, “Many-body transverse in- teractions in the quantum annealing of the p-spin ferro- magnet,” Journal of Physics A 45, 435301 (2012).
[90] T.Jo ̈rg,F.Krzakala,J.Kurchan,A.C.Maggs,and J. Pujos, “Energy gaps in quantum first-order mean- field–like transitions: The problems that quantum an- nealing cannot solve,” Europhys. Lett. 89, 40004 (2010).
[91] Tameem Albash, Victor Martin-Mayor, and Itay Hen, “Temperature scaling law for quantum annealing opti- mizers,” Physical Review Letters 119, 110502– (2017).
[92] Michele Filippone, S ́ebastien Dusuel, and Julien Vidal, “Quantum phase transitions in fully connected spin mod- els: An entanglement perspective,” Phys. Rev. A 83, 022327 (2011).

5

Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field
Authors: Yuki Susa, Yu Yamashiro, Masayuki Yamamoto, Hidetoshi Nishimori
https://arxiv.org/abs/1801.02005
(Submitted on 6 Jan 2018)
Phys. Rev. A. 99, 062307 (2019)

T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli, Science 284, 779
(1999).
E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D.
Preda, Science 292, 472 (2001).
G. E. Santoro, R. Martona ́k, E. Tosatti, and R. Car, Science 295, 2427
(2002).
G. E. Santoro and E. Tosatti, J. Phys. A 39, R393 (2006).
A. Das and B. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
S. Tanaka, R. Tamura, and B. K. Chakrabarti, Quantum Spin Glasses,
Annealing, and Computation (Cambridge University Press, 2017).
T. Albash and D. A. Lidar, arXiv:1705.07452.
J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S.
Lloyd, Nature 549, 195 (2017).
T. Albash and D. A. Lidar, arXiv:1611.04471.
E. Farhi, J. Goldstone, and S. Gutmann, arXiv:quant-ph/0208135.
E. Crosson, E. Farhi, C. Y.-Y. Lin, H.-H. Lin, and P. Shor,
arXiv:1401.7320.
H. Nishimori and K. Takada, Front. ICT 4, 2 (2017).
L. Hormozi, E. W. Brown, G. Carleo, and M. Troyer, Phys. Rev. B 95,
184416 (2017).
M. M. Rams, M. Mohseni, and A. del Campo, New J. Phys. 18, 123034
(2016).
T. Jo ̈rg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pujos, Europhys.
Lett. 89, 40004 (2010).
Y. Seki and H. Nishimori, Phys. Rev. E 85, 051112 (2012).
V. Bapst and G. Semerjian, J. Stat. Mech. 2012, P06007 (2012).
B. Seoane and H. Nishimori, J. Phys. A 45, 435301 (2012).
Y. Susa, J. F. Jadebeck, and H. Nishimori, Phys. Rev. A 95, 042321
(2017).
H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena (Oxford University Press, 2011).
M. Filippone, S. Dusuel, and J. Vidal, Phys. Rev. A 83, 022327 (2011).
T. Ichikawa, Master’s Thesis, Tokyo Insutitute of Technology (2014).
J. Johansson, P. Nation, and F. Nori, Comput. Phys. Commun. 183, 1760 (2012).
J. Johansson, P. Nation, and F. Nori, Comput. Phys. Commun. 184, 1234 (2013).

6

Quantum annealing with a nonvanishing final value of the transverse field
Authors: Kohji Nishimura, Hidetoshi Nishimori
https://arxiv.org/abs/1708.00236
(Submitted on 1 Aug 2017 (v1), last revised 10 Oct 2017 (this version, v2))
Phys. Rev. A 96, 042310 (2017)

[1] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355
(1998).
[2] J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli,
Science 284, 779 (1999).
[3] E. Farhi, J. Goldstone, S. Gutmann, J. Laplan, A. Lundgren, D. Preda, J. Lapan, A. Lundgren, D. Preda, J. Laplan, A. Lundgren, and D. Preda, Science 292, 472 (2001).
[4] G. E. Santoro, R. Martonák, E. Tosatti, and R. Car, Science 295, 2427 (2002).
[5] G. E. Santoro and E. Tosatti, J. Phys. A: Math. Gen. 39,
R393 (2006).
[6] A. Das and B. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
[7] S. Morita and H. Nishimori, J. Math. Phys. 49, 125210 (2008).
[8] S. Tanaka, R. Tamura, and B. K. Chakrabarti, Quantum Spin Glasses, Annealing, and Computation (Cambridge University Press, 2017).
[9] A. Lucas, Front. Phys. 2, 1 (2014).
[10] M. W. Johnson, M. H. S. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, A. J. Berkley, J. Jo- hansson, P. Bunyk, E. M. Chapple, C. Enderud, J. P. Hilton, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, C. J. S. Truncik, S. Uchaikin, J. Wang, B. Wilson, and G. Rose, Nature 473, 194 (2011).
[11] S. P. Jordan, E. Farhi, and P. W. Shor, Phys. Rev. A 74, 052322 (2006).
[12] D. A. Lidar, Phys. Rev. Lett. 100, 160506 (2008).
[13] G. Quiroz and D. A. Lidar, Phys. Rev. A 86, 042333 (2012).
[14] K. C. Young, M. Sarovar, and R. Blume-Kohout, Phys. Rev. X , 041013.
[15] M. Sarovar and K. C. Young, New J. of Phys. 15, 125032 (2013).
[16] A. Ganti, U. Onunkwo, and K. Young, Phys. Rev. A 89, 042313 (2014).
[17] K. C. Young, R. Blume-Kohout, and D. A. Lidar, Phys. Rev. A 88, 062314 (2013).
[18] A. D. Bookatz, E. Farhi, and L. Zhou, Phys. Rev. A 92, 022317 (2015).
[19] I. Marvian and D. A. Lidar, Phys. Rev. Lett. 113, 260504 (2014).
[20] Z. Jiang and E. G. Rieffel, arXiv:1511.01997 (2015).
[21] I. Marvian, arXiv:1602.03251 (2016).
[22] M. Marvian and D. Lidar, arXiv:1606.03795 (2016).
[23] K. L. Pudenz, T. Albash, and D. A. Lidar, Nat. Commun. 5, 3243 (2014).
[24] K. L. Pudenz, T. Albash, and D. A. Lidar, Phys. Rev.
A 91, 042302 (2015).
[25] W. Vinci, T. Albash, G. Paz-Silva, I. Hen, and D. A.
Lidar, Phys. Rev. A 92, 042310 (2015).
[26] A. Mishra, T. Albash, and D. A. Lidar, Quant. Inf. Proc.
15, 609 (2015).
[27] W. Vinci, T. Albash, and D. A. Lidar, Nature Quant.
Inf. 2, 16017 (2016).
[28] S. Matsuura, H. Nishimori, T. Albash, and D. A. Lidar,
Phys. Rev. Lett. 116, 220501 (2016).
[29] S. Matsuura, H. Nishimori, W. Vinci, T. Albash, and
D. A. Lidar, Phys. Rev. A 95, 022308 (2017).
[30] K. Nishimura, H. Nishimori, A. J. Ochoa, and H. G. Katzgraber, Phys. Rev. E. 94, 032105 (2016).
[31] Y. Otsubo, J. I. Inoue, K. Nagata, and M. Okada, Phys. Rev. E 86, 051138 (2012).
[32] H. Nishimori, Statistical Physics of Spin Glasses and In- formation Processing (Oxford University Press, 2001).
[33] P. Ruján., Phys. Rev. Lett. 70, 2968 (1993).
[34] S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
[35] S. R. White, Phys. Rev. B 48, 10345 (1993).
[36] J. Rodriguez-Laguna, J. Phys. A. Math. Theor. 40, 12043
(2007).
[37] J. Rodriguez-Laguna and S. N. Santalla, J. Stat. Mech.
07006 (2014).
[38] A. Viterbi., Information Theory, IEEE Transactions on
13, 260 (1967).
[39] D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35,
1792 (1975).
[40] H. F. Trotter, Proc. Amer. Math. Soc. 10, 545 (1959). [41] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976).
[42] The symbol σ2 for variance should not be confused with
the Pauli operator, the latter having a hat, such as σˆiz
[43] The behaviors of the overlap and the order parameters drawn in this figure are not reliable at low temperatures due to the replica symmetry breaking. Nevertheless, the existence of a peak in the overlap is likely to be estab- lished since the peak position is at a relatively high tem-
perature. √ 2
[44] Note that Dm ≡ (1/ 2π) exp (−m /2)dm denotes the
Gaussian measure.

7

Exact expression of the energy gap at first-order quantum phase transitions of a non-stoquastic Hamiltonian
Authors: Masaki Ohkuwa, Hidetoshi Nishimori
https://arxiv.org/abs/1707.07370 (Submitted on 24 Jul 2017)

References

T. Kadowaki and H. Nishimori: Phys. Rev. E 58 (1998) 5355.
T. Kadowaki: Dr. Thesis, Tokyo Institute of Technology (1998).
J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli: Science 284 (1999) 779.
G. E. Santoro, R. Martona ́k, E. Tosatti, and R. Car: Science 295 (2002) 2427.
G. E. Santoro and E. Tosatti: J. Phys. A: Math. Gen. 39 (2006) R393.
A. Das and B. Chakrabarti: Rev. Mod. Phys. 80 (2008) 1061.
S. Tanaka, R. Tamura, and B. K. Chakrabarti: Quantum Spin Glasses, Annealing, and Computation (Cambridge University Press, 2017).
S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi: Science 220 (1983).
T. F. Rønnow, Z. Wang, J. Job, S. Boixo, S. V. Isakov, D. Wecker, J. M. Martinis, D. A.
Lidar, and M. Troyer: Science 345 (2014) 420.
T. Albash and D. A. Lidar: arXiv:1705.07452 (2017).
A. Lucas: Frontiers in Phys. 2 (2014) 1.
H. Nishimori: Statistical Physics of Spin Glasses and Information Processing: An Intro- ducion (Oxford University Press, 2001).
E. Farhi, J. Goldstone, S. Gutmann, and S. Michael: arXiv:0001106 (2000).
E. Farhi, J. Goldstone, and S. Gutmann: arXiv:028135 (2002).
T. Albash and D. A. Lidar: arXiv:1611.04471 (2017).
S. Morita and H. Nishimori: J. Math. Phys. 49 (2008) 125210.
H. Nishimori and G. Ortiz: Elements of Phase Transitions and Critical Phenomena (Ox- ford University Press, 2011).
T. Jo ̈rg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pujos: EPL 89 (2010) 40004.
V. Bapst and G. Semerjian: J. Stat. Mech. 2012 (2012) P06007.
Y. Seki and H. Nishimori: Phy. Rev. E 85 (2012) 051112.
Y. Seki and H. Nishimori: J. Phys. A: Math. Theor. 48 (2015) 335301.
S. Bravyi, D. P. Di Vincenzo, R. Oliveira, and B. M. Terhal: Quanum Inf. Comput. 8 (2008) 361.
H. Nishimori and K. Takada: Frontiers in ICT 4 (2017) 2. 13/14
J. Phys. Soc. Jpn.
E. Farhi, D. Gosset, I. Hen, A. W. Sandvik, P. Shor, A. P. Young, and F. Zamponi: Phys. Rev. A 86 (2012) 052334.
E. Crosson, E. Farhi, C. Y.-y. Lin, H.-h. Lin, and P. Shor: arXiv:1401.7320 (2014).
L. Hormozi, E. W. Brown, G. Carleo, and M. Troyer: Physical Review B 95 (2017) 184416.
P. Braun: Rev. Mod. Phys. 65 (1993) 115.
A. Garg: J. Math. Phys. 39 (1998) 5166.
A. Garg: Phys. Rev. lett. 83 (1999) 4385.
K. Kechedzhi and V. N. Smelyanskiy: Phys. Rev. X 6 (2016) 021028.
S. V. Isakov, G. Mazzola, V. N. Smelyanskiy, Z. Jiang, S. Boixo, H. Neven, and M. Troyer: Phys. Rev. Lett. 117 (2016) 180402.
Z. Jiang, V. N. Smelyanskiy, S. V. Isakov, S. Boixo, G. Mazzola, M. Troyer, and H. Neven: Phys. Rev. A 95 (2017) 012322.
Y. Susa, J. F. Jadebeck, and H. Nishimori: Physical Review A 95 (2017) 042321.
B. Seoane and H. Nishimori: J. Phys. A: Math. Theor. 45 (2012) 435301.

8

Direct comparison of quantum and simulated annealing on a fully-connected Ising ferromagnet
Authors: Matteo M. Wauters, Rosario Fazio, Hidetoshi Nishimori, Giuseppe E. Santoro
https://arxiv.org/abs/1707.02621 (Submitted on 9 Jul 2017)

1 A. Lucas, Frontiers in Phys. 2, 1 (2014).
2 A. B. Finnila, M. A. Gomez, C. Sebenik, C. Stenson, and
J. D. Doll, Chem. Phys. Lett. 219, 343 (1994).
3 T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355
(1998).
4 J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli,
Science 284, 779 (1999).
5 G. E. Santoro, R. Martonˇ ́ak, E. Tosatti, and R. Car, Sci-
ence 295, 2427 (2002).
6 G. E. Santoro and E. Tosatti, J. Phys. A: Math. Gen. 39,
R393 (2006).
7 S. Morita and H. Nishimori, J. Math. Phys. 49, 125210
(2008).
8 E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lund-
gren, and D. Preda, Science 292, 472 (2001).
9 S. Kirkpatrick, J. C. D. Gelatt, and M. P. Vecchi, Science
220, 671 (1983).
10 R. Harris et al., Phys. Rev. B 82, 024511 (2010).
11 M. W. Johnson et al., Nature 473, 194 (2011).
12 T. F. Rønnow, Z. Wang, J. Job, S. Boixo, S. V. Isakov,
D. Wecker, J. M. Martinis, D. A. Lidar, and M. Troyer,
Science 345, 420 (2014).
13 R. Martonˇa ́k, G. E. Santoro, and E. Tosatti, Phys. Rev. B
66, 094203 (2002).
14 R. Martonˇa ́k, G. E. Santoro, and E. Tosatti, Phys. Rev. E
70, 057701 (2004).
15 D. A. Battaglia, G. E. Santoro, and E. Tosatti, Phys. Rev.
E 71, 066707 (2005).
16 L. Stella, G. E. Santoro, and E. Tosatti, Phys. Rev. B 72,
014303 (2005).
17 L. Stella, G. E. Santoro, and E. Tosatti, Phys. Rev. B 73,
144302 (2006).
18 Y. Matsuda, H. Nishimori, and H. G. Katzgraber, New J.
Phys. 11, 073021 (2009).
19 A. P. Young, S. Knysh, and V. N. Smelyanskiy, Phys. Rev.
Lett. 104, 020502 (2010).
20 I. Hen and A. P. Young, Phys. Rev. E 84, 061152 (2011).
21 E. Farhi, D. Gosset, I. Hen, A. W. Sandvik, P. Shor, A. P.
Young, and F. Zamponi, Phys. Rev. A 86, 052334 (2012).
22 S. Boixo, T. F. Rønnow, S. V. Isakov, Z. Wang, D. Wecker, D. A. Lidar, J. M. Martinis, and M. Troyer, Nature Physics
10, 218 (2014).
23 H. G. Katzgraber, F. Hamze, and R. S. Andrist, Phys.
Rev. X 4, 021008 (2014).
24 H. G. Katzgraber, F. Hamze, Z. Zhu, A. J. Ochoa, and
H. Munoz-Bauza, Phys. Rev. X 5, 031026 (2015).
25 T. Albash, T. Rønnow, M. Troyer, and D. Lidar, Euro.
Phys. J. Special Topics 224, 111 (2015).
26 B. Heim, T. F. Rønnow, S. V. Isakov, and M. Troyer, Sci-
ence 348, 215 (2015).
27 I. Hen, J. Job, J. Job, M. Troyer, and D. A. Lidar, Phys.
Rev. A 92, 042325 (2015).
28 S. V. Isakov, G. Mazzola, V. N. Smelyanskiy,
Z. Jiang, S. Boixo, H. Neven, and M. Troyer (2015),
arXiv:1510.08057.
29 V. Martin-Mayor and I. Hen, Sci. Rep. 5, 15324 (2015).
30 C.-W. Liu, A. Polkovnikov, and A. W. Sandvik, Phys. Rev.
Lett. 114, 147203 (2015).
31 D. S. Steiger, T. F. Rønnow, and M. Troyer, Phys. Rev.
Lett. 115, 230501 (2015).
32 D. Venturelli, S. Mandra, S. Knysh, B. O’Gorman, R. Biswas, and V. Smelyanskiy, Phys. Rev. X 5, 031040 (2015). 33 E. Crosson and A. W. Harrow (2016), arXiv:1601.03030. 34 V. S. Denchev, S. Boixo, S. V. Isakov, N. Ding, R. Bab- bush, V. Smelyanskiy, J. Martinis, and H. Neven, Phys. Rev. X 6, 031015 (2016). 35 K. Kechedzhi and V. N. Smelyanskiy, Phys. Rev. X 6, 021028 (2016). 36 S. Mandra, Z. Zhu, W. Wang, A. Perdomo-Ortiz, and H. G.
Katzgraber, Phys. Rev. A 94, 022337 (2016).
37 S. Mandra, Z. Zhu, and H. G. Katzgraber (2016), arXiv:1606.07146. 38 J. Marshall, V. Martin-Mayor, and I. Hen, Phys. Rev. A 94, 012320 (2016). 39 S. Muthukrishnan, T. Albash, and D. A. Lidar, Phys. Rev. X 6, 031010 (2016). 40 S. V. Isakov, G. Mazzola, V. N. Smelyanskiy, Z. Jiang, S. Boixo, H. Neven, and M. Troyer, Phys. Rev. Lett. 117, 180402 (2016). 41 T. Albash and D. A. Lidar, arXiv:1611.04471 (2017). 42 J. King, S. Yarkoni, J. Raymond, I. Ozfidan, A. D. King, M. M. Nevisi, J. P. Hilton, and C. C. McGeoch, arXiv:1701.04579 (2017). 43 S. Mandra, H. G. Katzgraber, and C. Thomas,
arXiv:1703.00622 (2017).
44 T. Albash and D. A. Lidar, arXiv:1705.07452 (2017).
45 Z. Jiang, V. N. Smelyanskiy, S. V. Isakov, S. Boixo,
G. Mazzola, M. Troyer, and H. Neven, Phys. Rev. A p.
012322 (2017).
46 D. Herr, E. Brown, B. Heim, M. Ko ̈nz, G. Mazzola, and
M. Troyer, arXiv:1704.00420 (2017).
47 L. K. Grover, Phys. Rev. Lett. 79, 325 (1997).
48 J. Roland and N. J. Cerf, Phys. Rev. A 65, 042308 (2002). 49 T. Jo ̈rg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pu-
jos, EPL 89, 40004 (2010).
50 T. Caneva, R. Fazio, and G. E. Santoro, Phys. Rev. B 78,
104426 (2008).
51 V. Bapst and G. Semerjian, JSTAT p. P06007 (2012).
52 H. Nishimori and K. Takada, Frontiers in ICT 4, 2 (2017). 53 Y. Seki and H. Nishimori, Phy. Rev. E 85, 051112 (2012). 54 B. Seoane and H. Nishimori, J. Phys. A: Math. Theor. 45,
435301 (2012).
55 Y. Susa, J. F. Jadebeck, and H. Nishimori, Physical Re-
view A 95, 042321 (2017).
56 H. Nishimori, J. Tsuda, and S. Knysh, Phys. Rev. E 91,
012104 (2015).
57 T. Zanca and G. E. Santoro, Phys. Rev. B 93, 224431
(2016).
58 R. J. Glauber, J. Math. Phys. 4, 294 (1963).
59 N. G. van Kampen, Stochastic processes in physics and
chemistry (North-Holland, 1992), Revised and enlarged ed. 60 S. Suzuki and M. Okada, J. Phys. Soc. Jpn. 74, 1649
(2005).
61 C. De Grandi, A. Polkovnikov, and A. W. Sandvik, Phys.
Rev. B 84, 224303 (2011).

9

Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic Hamiltonian
Authors: Yuki Susa, Johann F. Jadebeck, Hidetoshi Nishimori
https://arxiv.org/abs/1612.08265 (Submitted on 25 Dec 2016 (v1), last revised 19 Apr 2017 (this version, v2))

[1] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, New York, 1979).
[2] F. Barahona, On the computational complexity of the Ising spin glass models, J. Phys. A 15, 3241 (1982).
[3] T. Kadowaki and H. Nishimori, Quantum annealing in the trans- verse Ising model, Phys. Rev. E 58, 5355 (1998).
[4] T. Kadowaki, Study of optimization problems by quantum an- nealing, arXiv:quant-ph/0205020.
[5] A. B. Finnila, M. A. Gomez, C. Sebenick, C. Stenson, and J. D. Doll, Quantum annealing: A new method for minimizing mul- tidimensional functions, Chem. Phys. Lett. 219, 343 (1994).
[6] J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli, Quantum annealing of a disordered magnet, Science 284, 779 (1999).
[7] G. E. Santoro, R. Martonak, E. Tosatti, and R. Car,
Theory of quantum annealing of an Ising spin glass,
Science 295, 2427 (2002).
[8] G. E. Santoro and E. Tosatti, Optimization using quantum
mechanics: Quantum annealing through adiabatic evolution,
J. Phys. A 39, R393 (2006).
[9] A. Das and B. K. Chakrabarti, Colloquium: Quan-
tum annealing and analog quantum computation,
Rev. Mod. Phys. 80, 1061 (2008).
[10] S. Morita and H. Nishimori, Mathematical foundation of quan-
tum annealing, J. Math. Phys. 49, 125210 (2008).
[11] S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Optimization by
simulated annealing, Science 220, 671 (1983).
[12] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lund- gren, and D. Preda, A quantum adiabatic evolution algo- rithm applied to random instances of an NP-complete problem, Science 292, 472 (2001); E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, Quantum computation by adiabatic evolution,
arXiv:quant-ph/0001106.
[13] T. Albash and D. A. Lidar, Adiabatic quantum computing,
arXiv:1611.04471.
[14] T. Jörg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pujos,
Energy gaps in quantum first-order mean-fieldâĂŞlike tran- sitions: The problems that quantum annealing cannot solve, Europhys. Lett. 89, 40004 (2010).
[15] Y. Seki and H. Nishimori, Quantum annealing with antiferro- magnetic fluctuations, Phys. Rev. E 85, 051112 (2012).
[16] B. Seoane and H. Nishimori, Many-body transverse interac- tions in the quantum annealing of the p-spin ferromagnet, J. Phys. A 45, 435301 (2012).
[17] Y. Seki and H. Nishimori, Quantum annealing with anti- ferromagnetic transverse interactions for the Hopfield model, J. Phys. A 48, 335301 (2015).
[18] S. Bravyi, D. P. Di Vincenzo, R. Oliveira, and B. M. Terhal, The complexity of stoquastic local Hamiltonian problems, Quantum Inf. Comput. 8, 361 (2008).
[19] M. Suzuki, Relationship between d-dimensional quan- tal spin systems and (d + 1)-dimensional Ising systems, Prog. Theor. Phys. 56, 1454 (1976).
[20] H. Nishimori and K. Takada, Exponential enhancement of the efficiency of quantum annealing by non-stoquastic Hamiltoni-
ans, Front. ICT 4, 2 (2017).
[21] E. Farhi, J. Goldstone, and S. Gutmann, Quantum adiabatic
evolution algorithms with different paths, arXiv:0208135.
[22] E. Crosson, E. Farhi, C. Y. -Y Lin, H. -H. Lin, and P. Shor, Different strategies for optimization using the quantum adiabatic
algorithm, arXiv:1401.7320.
[23] L. Hormozi, E. W. Brown, G. Carleo, and M. Troyer, Non-
stoquastic Hamiltonians and quantum annealing of Ising spin
glass, arXiv:1609.06558.
[24] S. Muthukrishnan, T. Albash, and D. A. Lidar, Tunneling and
Speedup in Quantum Optimization for Permutation-Symmetric
Problems, Phys. Rev. X 6, 031010 (2016).
[25] E. Farhi, J. Goldstone, and S. Gutmann, Quantum Adi-
abatic Evolution Algorithms versus Simulated Annealing,
arXiv:0201031.
[26] G. Schaller and R. Schützhold, The role of symmetries in adi-
abatic quantum algorithms, Quantum Inf. Comput. 10, 0109
(2010).
[27] S. Boixo, V. N. Smelyanskiy, A. Shabani, S. V. Isakov,
M. Dykman, V. S. Denchev, M. H. Amin, A. Y. Smirnov, M. Mohseni, and H. Neven, Computational multiqubit tunneling in programmable quantum annealers, Nature Commun. 7, 10327 (2016).
[28] M. Filippone, S. Dusuel, and J. Vidal, Quantum phase transitions in fully connected spin models: An entanglement perspective, Phys. Rev. A 83, 022327 (2011).
[29] Notice that Ref. [28] finds an exceptional case where a first-order transition is accompanied by a sharp peak or a divergence in en- tanglement measures as in the case of second-order transitions.
[30] S. Hill and W. K. Wootters, Entanglement of a Pair of Quantum Bits, Phys. Rev. Lett. 78, 5022 (1997).
[31] W. K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubits, Phys. Rev. Lett. 80, 2245 (1998).
[32] H. Yano and H. Nishimori, Ground state entanglement in spin systems, Prog. Theor. Phys. Suppl. 157, 164 (2005).
[33] X. Wang and B. C. Sanders, Spin squeezing and pairwise entanglement for symmetric multiqubit states,
Phys. Rev. A 68, 012101 (2003).
[34] J. Vidal,
glement in
Phys. Rev. A
R. Mosseri, and J. Dukelsky, Entan-
a first-order quantum phase transition, 69, 054101 (2004).
[35] J. Vidal,Concurrence in collective models, 73, 063218 (2006).
[36] L.-A. Wu, M. S. Sarandy, D. A. Lidar, and L. J. Sham, Linking entanglement and quantum phase transitions via density-functional theory,
Phys. Rev. A 74, 052335 (2006).M. S. Sarandy, and D. A. Lidar, Quan- Transitions and Bipartite Entanglement, Phys. Rev. Lett. 93, 250404 (2004);
[37] L. T. Brady and W. van Dam, Necessary adiabatic run times in
quantum optimization, Phys. Rev. A 95, 032335 (2017).
[38] B. Bauer, L. Wang, I. Pizorn, and M. Troyer, Entanglement as a resource in adiabatic quantum optimization arXiv:1501.06914.
[39] P. Hauke, L. Bonnes, M. Heyl, and W. Lechner, Probing entan- glement in adiabatic quatnum optimization with trapped ions,
Front. in Phys. 3, 21 (2015).

10

Quantum annealing correction at finite temperature: ferromagnetic p-spin models
Authors: Shunji Matsuura, Hidetoshi Nishimori, Walter Vinci, Tameem Albash, Daniel A. Lidar
https://arxiv.org/abs/1610.09535 (Submitted on 29 Oct 2016)

[1] A. B. Finnila, M. A. Gomez, C. Sebenik, C. Stenson, and J. D. Doll, “Quantum annealing: A new method for min- imizing multidimensional functions,” Chemical Physics Letters 219, 343–348 (1994).
[2] Tadashi Kadowaki and Hidetoshi Nishimori, “Quantum annealing in the transverse Ising model,” Phys. Rev. E 58, 5355 (1998).
[3] Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Joshua Lapan, Andrew Lundgren, and Daniel Preda, “A Quan- tum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem,” Science 292, 472–475 (2001).
[4] J. Brooke, T. F. Rosenbaum, and G. Aeppli, “Tunable quantum tunnelling of magnetic domain walls,” Nature
that the penalty transverse field increases the potential barrier between m = 0 and mlarge, and may remove the additional local minimum msmall.
413, 610–613 (2001).
[5] GiuseppeE.Santoro,RomanMartonˇa ́k,ErioTosatti,
and Roberto Car, “Theory of quantum annealing of an
Ising spin glass,” Science 295, 2427–2430 (2002).
[6] Arnab Das and Bikas K. Chakrabarti, “Colloquium: Quantum annealing and analog quantum computation,”
Rev. Mod. Phys. 80, 1061–1081 (2008).
[7] T. Kato, “On the adiabatic theorem of quantum mechan-
ics,” J. Phys. Soc. Jap. 5, 435 (1950).
[8] Sabine Jansen, Mary-Beth Ruskai, and Ruedi Seiler,
“Bounds for the adiabatic approximation with appli- cations to quantum computation,” J. Math. Phys. 48, 102111 (2007).
[9] Daniel A. Lidar, Ali T. Rezakhani, and Alioscia Hamma,
“Adiabatic approximation with exponential accuracy for many-body systems and quantum computation,” J. Math. Phys. 50, 102106 (2009).
[10] Andrew M. Childs, Edward Farhi, and John Preskill, “Robustness of adiabatic quantum computation,” Phys. Rev. A 65, 012322 (2001).
[11] M. S. Sarandy and D. A. Lidar, “Adiabatic quantum computation in open systems,” Phys. Rev. Lett. 95, 250503– (2005).
[12] M. H. S. Amin, Peter J. Love, and C. J. S. Truncik, “Thermally assisted adiabatic quantum computation,” Phys. Rev. Lett. 100, 060503 (2008).
[13] M. H. S. Amin, Dmitri V. Averin, and James A. Nesteroff, “Decoherence in adiabatic quantum computa- tion,” Phys. Rev. A 79, 022107 (2009).
[14] Tameem Albash, Sergio Boixo, Daniel A Lidar, and Paolo Zanardi, “Quantum adiabatic markovian master equations,” New J. of Phys. 14, 123016 (2012).
[15] Tameem Albash and Daniel A. Lidar, “Decoherence in adiabatic quantum computation,” Phys. Rev. A 91, 062320– (2015).
[16] S. P. Jordan, E. Farhi, and P. W. Shor, “Error-correcting codes for adiabatic quantum computation,” Phys. Rev. A 74, 052322 (2006).
[17] D. A. Lidar, “Towards fault tolerant adiabatic quantum computation,” Phys. Rev. Lett. 100, 160506 (2008).
[18] G. Quiroz and D. A. Lidar, “High-fidelity adiabatic quan-
tum computation via dynamical decoupling,” Phys. Rev.
A 86, 042333 (2012).
[19] Kevin C. Young, Mohan Sarovar, and Robin Blume-
Kohout, “Error suppression and error correction in adi- abatic quantum computation: Techniques and chal- lenges,” Phys. Rev. X 3, 041013– (2013).
[20] Mohan Sarovar and Kevin C Young, “Error suppression and error correction in adiabatic quantum computation: non-equilibrium dynamics,” New J. of Phys. 15, 125032 (2013).
[21] Anand Ganti, Uzoma Onunkwo, and Kevin Young, “Family of [[6k,2k,2]] codes for practical, scalable adia- batic quantum computation,” Phys. Rev. A 89, 042313– (2014).
[22] Kevin C. Young, Robin Blume-Kohout, and Daniel A. Lidar, “Adiabatic quantum optimization with the wrong hamiltonian,” Phys. Rev. A 88, 062314– (2013).
[23] Adam D. Bookatz, Edward Farhi, and Leo Zhou, “Error suppression in hamiltonian-based quantum computation using energy penalties,” Physical Review A 92, 022317– (2015).
[24] Iman Marvian and Daniel A. Lidar, “Quantum error sup- pression with commuting hamiltonians: Two local is too local,” Phys. Rev. Lett. 113, 260504– (2014).
[25] Zhang Jiang and Eleanor G. Rieffel, “Non-commuting two-local hamiltonians for quantum error suppression,” arXiv:1511.01997 (2015).
[26] Iman Marvian, “Exponential suppression of decoher- ence and relaxation of quantum systems using energy penalty,” arXiv:1602.03251 (2016).
[27] Milad Marvian and Daniel Lidar, “Error suppression for hamiltonian-based quantum computation using subsys- tem codes,” arXiv:1606.03795 (2016).
[28] P. Aliferis, D. Gottesman, and J. Preskill, “Quantum accuracy threshold for concatenated distance-3 codes,” Quantum Inf. Comput. 6, 97 (2006).
[29] Ari Mizel, “Fault-tolerant, universal adiabatic quantum
computation,” arXiv:1403.7694 (2014).
[30] M. W. Johnson, M. H. S. Amin, S. Gildert, T. Lanting,
F. Hamze, N. Dickson, R. Harris, A. J. Berkley, J. Jo- hansson, P. Bunyk, E. M. Chapple, C. Enderud, J. P. Hilton, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, C. J. S. Truncik, S. Uchaikin, J. Wang, B. Wilson, and G. Rose, “Quantum annealing with manufactured spins,” Nature 473, 194–198 (2011).
[31] R. Harris, M. W. Johnson, T. Lanting, A. J. Berkley, J. Johansson, P. Bunyk, E. Tolkacheva, E. Ladizinsky, N. Ladizinsky, T. Oh, F. Cioata, I. Perminov, P. Spear, C. Enderud, C. Rich, S. Uchaikin, M. C. Thom, E. M. Chapple, J. Wang, B. Wilson, M. H. S. Amin, N. Dickson, K. Karimi, B. Macready, C. J. S. Truncik, and G. Rose, “Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor,” Phys. Rev. B 82, 024511 (2010).
[32] P. I Bunyk, E. M. Hoskinson, M. W. Johnson, E. Tolka- cheva, F. Altomare, AJ. Berkley, R. Harris, J. P. Hilton, T. Lanting, AJ. Przybysz, and J. Whittaker, “Archi- tectural considerations in the design of a superconduct- ing quantum annealing processor,” IEEE Transactions on Applied Superconductivity 24, 1–10 (Aug. 2014).
[33] Sergio Boixo, Troels F. Ronnow, Sergei V. Isakov, Zhihui Wang, David Wecker, Daniel A. Lidar, John M. Martinis, and Matthias Troyer, “Evidence for quantum annealing with more than one hundred qubits,” Nat. Phys. 10, 218– 224 (2014).
[34] Seung Woo Shin, Graeme Smith, John A. Smolin, and Umesh Vazirani, “How “quantum” is the D-Wave ma- chine?” arXiv:1401.7087 (2014).
[35] T. Albash, T. F. Rønnow, M. Troyer, and D. A. Lidar, “Reexamining classical and quantum models for the d- wave one processor,” Eur. Phys. J. Spec. Top. 224, 111– 129 (2015).
[36] P. J. D. Crowley, T. Duri ́c, W. Vinci, P. A. Warbur- ton, and A. G. Green, “Quantum and classical dynam- ics in adiabatic computation,” Phys. Rev. A 90, 042317– (2014).
[37] Walter Vinci, Klas Markstr ̈om, Sergio Boixo, Aidan Roy, Federico M. Spedalieri, Paul A. Warburton, and Simone Severini, “Hearing the shape of the ising model with a programmable superconducting-flux annealer,” Sci. Rep. 4 (2014).
[38] Victor Martin-Mayor and Itay Hen, “Unraveling quan- tum annealers using classical hardness,” Scientific Re- ports 5, 15324 EP – (2015).
[39] Kristen L Pudenz, Tameem Albash, and Daniel A Li- dar, “Error-corrected quantum annealing with hundreds of qubits,” Nat. Commun. 5, 3243 (2014).
[40] Kristen L. Pudenz, Tameem Albash, and Daniel A. Li- dar, “Quantum annealing correction for random Ising problems,” Phys. Rev. A 91, 042302 (2015).
[41] Walter Vinci, Tameem Albash, Gerardo Paz-Silva, Itay Hen, and Daniel A. Lidar, “Quantum annealing correc- tion with minor embedding,” Phys. Rev. A 92, 042310– (2015).
[42] Anurag Mishra, Tameem Albash, and Daniel A. Lidar, “Performance of two different quantum annealing correc- tion codes,” Quant. Inf. Proc. 15, 609–636 (2015).
[43] Walter Vinci, Tameem Albash, and Daniel A Lidar, “Nested quantum annealing correction,” Nature Quan- tum Information 2, 16017 (2016).
[44] Shunji Matsuura, Hidetoshi Nishimori, Walter Vinci, Tameem Albash, and Daniel A. Lidar, in preparation.
[45] Shunji Matsuura, Hidetoshi Nishimori, Tameem Albash, and Daniel A. Lidar, “Mean field analysis of quan- tum annealing correction,” Physical Review Letters 116, 220501– (2016).
[46] G. G. Cabrera and R. Jullien, “Role of boundary con- ditions in the finite-size ising model,” Phys. Rev. B 35 (1987).
[47] Junichi Tsuda, Yuuki Yamanaka, and Hidetoshi Nishi- mori, “Energy gap at first-order quantum phase transi- tions: An anomalous case,” Journal of the Physical So- ciety of Japan, Journal of the Physical Society of Japan 82, 114004 (2013).
[48] F Barahona, “On the computational complexity of Ising spin glass models,” J. Phys. A: Math. Gen 15, 3241 (1982).
[49] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Opti- mization by simulated annealing,” Science 220, 671–680 (1983).
[50] Alain Joye, “General Adiabatic Evolution with a Gap Condition,” Commun. Math. Phys. 275, 139–162 (2007).
[51] Ognyan Oreshkov and John Calsamiglia, “Adiabatic Markovian Dynamics,” Phys. Rev. Lett. 105, 050503
(2010).
[52] J. E. Avron, M. Fraas, G. M. Graf, and P. Grech, “Adia-
batic theorems for generators of contracting evolutions,”
Comm. Math. Phys. 314, 163–191 (2012).
[53] Lorenzo Campos Venuti, Tameem Albash, Daniel A. Li- dar, and Paolo Zanardi, “Adiabaticity in open quantum
systems,” Physical Review A 93, 032118– (2016).
[54] D. Gottesman, “Class of quantum error-correcting codes saturating the quantum hamming bound,” Phys. Rev. A
54, 1862 (1996).
[55] Masuo Suzuki, “Relationship between d-dimensional
quantal spin systems and (d+1)-dimensional ising sys- tems: Equivalence, critical exponents and systematic ap- proximants of the partition function and spin correla- tions,” Progress of Theoretical Physics 56, 1454–1469 (1976).
[56] T.Jo ̈rg,F.Krzakala,J.Kurchan,A.C.Maggs,and J. Pujos, “Energy gaps in quantum first-order mean- field–like transitions: The problems that quantum an- nealing cannot solve,” Europhys. Lett. 89, 40004 (2010).
[57] Sergey Knysh, “Zero-temperature quantum annealing bottlenecks in the spin-glass phase,” Nat Commun 7 (2016).

11

Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
Hidetoshi Nishimori, Kabuki Takada
(Submitted on 13 Sep 2016 (v1), last revised 18 Feb 2017 (this version, v3))
https://arxiv.org/abs/1609.03785
Frontiers in ICT 4, 2 (2017)

[1] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[2] T. Kadowaki, Ph.D. thesis, Tokyo Institute of Technology (1998), arXiv:quant-ph/0205020.
[3] J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli, Science 284, 779 (1999).
[4] E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser (2000), arXiv:quant-ph/0001106.
[5] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science 292, 472 (2001). [6] G. E. Santoro and R. Marton, Science 295, 2427 (2002).
[7] G. E. Santoro and E. Tosatti, J. Phys. A: Math. Gen. 39, R393 (2006).
[8] A. Das and B. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
[9] S. Morita and H. Nishimori, J. Math. Phys. 49, 125210 (2008).
[10] A. Lucas, Frontiers in Phys. 2, 1 (2014).
[11] S. Boixo, T. F. Rønnow, S. V. Isakov, Z. Wang, D. Wecker, D. A. Lidar, J. M. Martinis, and M. Troyer, Nature Physics 10, 218 (2014).
[12] T. F. Rønnow, Z. Wang, J. Job, S. Boixo, S. V. Isakov, D. Wecker, J. M. Martinis, D. A. Lidar, and M. Troyer, Science 345, 420 (2014).
[13] H. G. Katzgraber, F. Hamze, and R. S. Andrist, Phys. Rev. X 4, 021008 (2014).
[14] I. Hen, J. Job, J. Job, M. Troyer, and D. A. Lidar, Phys. Rev. A 92, 042325 (2015).
[15] B. Heim, T. F. Rønnow, S. V. Isakov, and M. Troyer, Science 348, 215 (2015).
[16] S. V. Isakov, G. Mazzola, V. N. Smelyanskiy, Z. Jiang, S. Boixo, H. Neven, and M. Troyer (2015), arXiv:1510.08057.
[17] D. Venturelli, S. Mandra, S. Knysh, B. O’Gorman, R. Biswas, and V. Smelyanskiy, Phys. Rev. X 5, 031040 (2015). [18] H. G. Katzgraber, F. Hamze, Z. Zhu, A. J. Ochoa, and H. Munoz-Bauza, Phys. Rev. X 5, 031026 (2015). [19] D. S. Steiger, T. F. Rønnow, and M. Troyer, Phys. Rev. Lett. 115, 230501 (2015). [20] T. Albash, T. Rønnow, M. Troyer, and D. Lidar, Euro. Phys. J. Special Topics 224, 111 (2015). [21] V. Martin-Mayor and I. Hen, Sci. Rep. 5, 15324 (2015). [22] S. Muthukrishnan, T. Albash, and D. A. Lidar, Phys. Rev. X 6, 031010 (2016). [23] K. Kechedzhi and V. N. Smelyanskiy, Phys. Rev. X 6, 021028 (2016). [24] V. S. Denchev, S. Boixo, S. V. Isakov, N. Ding, R. Babbush, V. Smelyanskiy, J. Martinis, and H. Neven, Phys. Rev. X 6, 031015 (2016). [25] S. Mandra, Z. Zhu, W. Wang, A. Perdomo-Ortiz, and H. G. Katzgraber, Phys. Rev. A 94, 022337 (2016).
[26] J. Marshall, V. Martin-Mayor, and I. Hen, Phys. Rev. A 94, 012320 (2016).
[27] Y. Matsuda, H. Nishimori, and H. G. Katzgraber, New J. Phys. 11, 073021 (2009).
[28] S. Mandra`, Z. Zhu, and H. G. Katzgraber (2016), arXiv:1606.07146.
[29] E. Crosson and A. W. Harrow (2016), arXiv:1601.03030.
[30] A. P. Young, S. Knysh, and V. N. Smelyanskiy, Phys. Rev. Lett. 104, 020502 (2010).
[31] I. Hen and A. P. Young, Phys. Rev. E 84, 061152 (2011).
[32] E. Farhi, D. Gosset, I. Hen, A. W. Sandvik, P. Shor, A. P. Young, and F. Zamponi, Phys. Rev. A 86, 052334 (2012).
[33] Z. Jiang, V. N. Smelyanskiy, S. V. Isakov, S. Boixo, G. Mazzola, M. Troyer, and H. Neven (2016), arXiv:1603.01293.
[34] S. Morita and H. Nishimori, J. Phys. Soc. Jpn. 76, 064002 (2007).
[35] R. Somma, C. Batista, and G. Ortiz, Phys. Rev. Lett. 99, 030603 (2007).
[36] S. Morita and H. Nishimori, J. Phys. A: Math. Gen. 39, 13903 (2006).
[37] S. Geman and D. Geman, IEEE Trans. Pattern Analy. Mech. Intell. PAMI-6, 721 (1984).
[38] S. Bravyi, D. P. Di Vincenzo, R. Oliveira, and B. M. Terhal, Quanum Inf. Comput. 8, 361 (2008).
[39] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976).
[40] J. Biamonte and P. Love, Phys. Rev. A 78, 012352 (2008).
[41] E. Farhi, J. Goldstone, and S. Gutmann (2002), arXiv:0208135.
[42] E. Crosson, E. Farhi, C. Y.-y. Lin, H.-h. Lin, and P. Shor (2014), arXiv:1401.7320.
[43] L. Hormozi, E. W. Brown, G. Carleo, and M. Troyer (2016), arXiv:1609.06558.
[44] Y. Seki and H. Nishimori, Phy. Rev. E 85, 051112 (2012).
[45] Y. Seki and H. Nishimori, J. Phys. A: Math. Theor. 48, 335301 (2015).
[46] B. Seoane and H. Nishimori, J. Phys. A: Math. Theor. 45, 435301 (2012).
[47] S. Jansen, M.-B. Ruskai, and R. Seiler, J. Math. Phys. 48, 102111 (2007).
[48] D. A. Lidar, A. T. Rezakhani, and A. Hamma, J. Math. Phys. 50, 102106 (2009).
[49] A. Elgart and G. A. Hagedorn, J. Math. Phys. 53, 1020 (2012).
[50] T. Jo ̈rg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pujos, EPL 89, 40004 (2010).
[51] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220 (1983).
[52] Y. Susa, J. F. Jadebeck, and H. Nishimori (2016), arXiv:1612.08265.
[53] H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena (Oxford University Press, 2011).
[54] A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).
[55] H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2002).
[56] S. Sinha and S. Dattagupta, Euro. Phys. J. B 86, 96 (2013).
[57] D. J. Amit, H. Gutfreund, and H. Sompolinsky, Phys. Rev. Lett. 55, 1530 (1985).
[58] D. J. Amit, H. Gutfreund, and H. Sompolinsky, Phys. Rev. A 32, 1007 (1985).
[59] D. J. Amit, H. Gutfreund, and H. Sompolinsky, Ann. Phys. 67, 30 (1987).
[60] H. Nishimori and Y. Nonomura, J. Phys. Soc. Jpn. 65, 3780 (1996).
[61] J. A. Smolin and G. Smith, Front. Phys. 2, 52 (2014).
[62] S. A. Owerre and M. B. Paranjape, Phys. Rep. 546, 33 (2014).
[63] T. Ichikawa, Master’s thesis, Tokyo Institute of Technology (2014).
[64] M. Okuyama, K. Nishimura, and H. Nishimori, in preparation (2016).
[65] M. B. Hastings and M. Freedman, Quantum Inf. Comp. 13, 1038 (2013).
[66] M. Jarret, S. P. Jordan, and B. Lackey (2016), arXiv:1607.03389.
[67] S. Knysh, Nature Commun. 7, 12370 (2016).
[68] H. Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introducion (Oxford University Press,
2001).
[69] It is to be noticed that, in some cases, it is non-trivial to efficiently simulate a stoquastic Hamiltonian. See, for example, [65, 66].
[70] It has been pointed out in [67] that a different type of difficulty exists within the spin glass phase of the Hopfield model when the random variables ξiμ are Gaussian-distributed, not binary as in the present paper.
[71] Notice that the replica symmetric ansatz [68] is used in the calculations. Our experience in the simple quantum Hopfield model in a transverse field suggests that the replica symmetry breaking takes place only in a very limited region in the phase diagram [60], and we expect it to be reasonable to assume a similar situation in the present case as well.

12

Retrieving the ground state of spin glasses using thermal noise: Performance of quantum annealing at finite temperatures
Kohji Nishimura, Hidetoshi Nishimori, Andrew J. Ochoa, Helmut G. Katzgraber
(Submitted on 11 May 2016 (v1), last revised 3 Sep 2016 (this version, v2))
Phys. Rev. E 94, 032105 (2016)
https://arxiv.org/abs/1605.03303

[1] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[2] T. Kadowaki, Study of Optimization Problems by Quan- tum Annealing, Ph.D. thesis, Tokyo Institute of Technol- ogy (1998).
[3] A. Finnila, M. Gomez, C. Sebenik, C. Stenson, and J. Doll, Chem. Phys. Lett. 219, 343 (1994).
[4] A. Das and B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
[5] G. E. Santoro and E. Tosatti, J. Phys. A 39, R393 (2006).
[6] S. Morita and H. Nishimori, J. Math. Phys. 49, 125210
(2008).
[7] V. Bapst, L. Foini, F. Krzakala, G. Semerjian, and
F. Zamponi, Phys. Rep. 523, 127 (2013).
[8] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lund-
gren, and D. Preda, Science 292, 472 (2001).
[9] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science
220, 671 (1983).
[10] A. Lucas, Front. Phys. 2, 5 (2014), 1302.5843 .
[11] M. W. Johnson, M. H. S. Amin, S. Gildert, T. Lanting,
F. Hamze, N. Dickson, R. Harris, A. J. Berkley, J. Jo- hansson, P. Bunyk, E. M. Chapple, C. Enderud, J. P. Hilton, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, C. J. S. Truncik, S. Uchaikin, J. Wang, B. Wilson, and G. Rose, Nature 473, 194 (2011).
[12] S. Boixo, T. Albash, F. M. Spedalieri, N. Chancellor, and D. a. Lidar, Nature Commun. 4, 2067 (2013).
[13] T. Lanting, A. J. Przybysz, A. Y. Smirnov, F. M. Spedalieri, M. H. Amin, a. J. Berkley, R. Harris, F. Al- tomare, S. Boixo, P. Bunyk, N. Dickson, C. Enderud, J. P. Hilton, E. Hoskinson, M. W. Johnson, E. Ladizin- sky, N. Ladizinsky, R. Neufeld, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, S. Uchaikin, a. B. Wilson, and G. Rose, Phys. Rev. X 4, 021041 (2014).
[14] T. Albash, W. Vinci, A. Mishra, P. A. Warburton, and
tion (Cambridge University Press, Cambride, UK, 2013).
D. A. Lidar, Phys. Rev. A 91, 042314 (2015).
[15] S. Boixo, V. N. Smelyanskiy, A. Shabani, S. V. Isakov, M. Dykman, V. S. Denchev, M. H. Amin, A. Y. Smirnov, M. Mohseni, and H. Neven, Nature Commun. 7, 10327 (2016).
[16] N. G. Dickson, M. W. Johnson, M. H. Amin, R. Harris,
F. Altomare, A. J. Berkley, P. Bunyk, J. Cai, E. M. Chap- ple, P. Chavez, F. Cioata, T. Cirip, P. deBuen, M. Drew- Brook, C. Enderud, S. Gildert, F. Hamze, J. P. Hilton, E. Hoskinson, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Lanting, T. Mahon, R. Neufeld, T. Oh, I. Perminov, C. Petroff, A. Przybysz, C. Rich, P. Spear, A. Tcaciuc, M. C. Thom, E. Tolkacheva, S. Uchaikin, J. Wang, A. B. Wilson, Z. Merali, and G. Rose, Nature Commun. 4, 1903 (2013).
[17] S. Boixo, T. F. Rønnow, S. V. Isakov, W. Zhihui, D. Wecker, D. A. Licar, J. M. Martinis, and M. Troyer, Nature Phys. 10, 218 (2014).
[18] T. Albash, T. Rønnow, M. Troyer, and D. Lidar, Eur. Phys. J. Special Topics 224, 111 (2015).
[19] P. J. D. Crowley, T. Ðurić, W. Vinci, P. A. Warburton, and A. G. Green, Phys. Rev. A 90, 042317 (2014).
[20] H. G. Katzgraber, F. Hamze, Z. Zhu, A. J. Ochoa, and
H. Munoz-Bauza, Phys. Rev. X 5, 031026 (2015).
[21] S. Mandrà, Z. Zhu, W. Wang, A. Perdomo-Ortiz, and H. G. Katzgraber, “Strengths and Weaknesses of Weak-Strong Cluster Problems: A Detailed Overview of State-of-the-art Classical Heuristics vs Quantum Ap-
proaches,” (2016).
[22] A. Perdomo-Ortiz, B. O’Gorman, J. Fluegemann,
R. Biswas, and V. N. Smelyanskiy, Sci. Rep. 6, 18628
(2015).
[23] Z. Zhu, A. J. Ochoa, S. Schnabel, F. Hamze, and H. G.
Katzgraber, Phys. Rev. A 93, 012317 (2016).
[24] D. A. Lidar, Phys. Rev. Lett. 100, 160506 (2008).
[25] D. A. Lidar and T. A. Brun, eds., Quantum Error Correction (Cambridge University Press, Cambride, UK, 2013).
[26] K. L. Pudenz, T. Albash, and D. A. Lidar, Nat. Com-
mun. 5, 3243 (2014).
[27] K. L. Pudenz, T. Albash, and D. A. Lidar, Phys. Rev.
A 91, 042302 (2015).
[28] W. Vinci, T. Albash, G. Paz-Silva, I. Hen, and D. A.
Lidar, Phys. Rev. A 92, 042310 (2015).
[29] N. Sourlas, Nature 339, 693 (1989).
[30] H. Nishimori, Statistical Physics of Spin Glasses and In-
formation Processing: An Introduction (Oxford Univer- sity Press, 2001).
[31] P. Ruján., Phys. Rev. Lett. 70, 2968 (1993).
[32] H. Nishimori, J. Phys. Soc. Jpn 62, 2973 (1993).
[33] N. Sourlas, EPL 25, 159 (1994).
[34] Y. Iba, J. Phys. A 32, 3875 (1999).
[35] N. Chancellor, S. Szoke, W. Vinci, G. Aeppli, and P. A.
Warburton, Sci. Rep. 6, 22318 (2016).
[36] A. Viterbi., IEEE Trans. Info. Theor. 13, 260 (1967).
[37] D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35,
1792 (1975). √
[38] Note that Dm ≡ exp(−m2/2)/ 2πdm represents the
Gaussian measure.

13

Critical properties of dissipative quantum spin systems in finite dimensions
Kabuki Takada, Hidetoshi Nishimori
(Submitted on 26 Feb 2016 (v1), last revised 5 Oct 2016 (this version, v2))
https://arxiv.org/abs/1602.08187
J. Phys. A: Math. Theor. 49 (2016) 435001

[1] A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1 (1987).
[2] U. Weiss, Quantum Dissipative Systems, 4th ed. (World Scientific, Singapore, 2012).
[3] A. Perdomo-Ortiz, B. O. Gorman, R. Biswas, and V. N. Smelyanskiy, “Determination and correction of persistent biases
in quantum annealers,” arXiv:1503.05679 .
[4] M. Benedetti, J. Realpe-G ́omez, R. Biswas, and A. Perdomo-Ortiz, “Estimation of effective temperatures in a quantum
annealer and its impact in sampling applications: A case study towards deep learning applications,” arXiv:1510.07611 .
[5] N. G. Dickson, M. W. Johnson, M. H. Amin, R. Harris, F. Altomare, A. J. Berkley, P. Bunyk, J. Cai, E. M. Chapple, P. Chavez, F. Cioata, T. Cirip, P. deBuen, M. Drew-Brook, C. Enderud, S. Gildert, F. Hamze, J. P. Hilton, E. Hoskinson, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Lanting, T. Mahon, R. Neufeld, T. Oh, I. Perminov, C. Petroff, A. Przybysz, C. Rich, P. Spear, A. Tcaciuc, M. C. Thom, E. Tolkacheva, S. Uchaikin, J. Wang, A. B. Wilson, Z. Merali, and G. Rose,
“Thermally assisted quantum annealing of a 16-qubit problem,” Nat. Commun. 4, 1903 (2013).
[6] V. N. Smelyanskiy, D. Venturelli, A. Perdomo-Ortiz, S. Knysh, and M. I. Dykman, “Quantum annealing via environment-
mediated quantum diffusion,” arXiv:1511.02581 .
[7] J. A. Hertz, “Quantum critical phenomena,” Phys. Rev. B 14, 1165 (1976).
[8] L. F. Cugliandolo, D. R. Grempel, G. Lozano, H. Lozza, and C. A. da Silva Santos, “Dissipative effects on quantum glassy
systems,” Phys. Rev. B 66, 014444 (2002).
[9] L. F. Cugliandolo, D. R. Grempel, G. Lozano, and H. Lozza, “Effects of dissipation on disordered quantum spin models,”
Phys. Rev. B 70, 024422 (2004).
[10] L. F. Cugliandolo, G. S. Lozano, and H. Lozza, “Static properties of the dissipative random quantum Ising ferromagnetic
chain,” Phys. Rev. B 71, 224421 (2005).
[11] M. Vojta, N.-H. Tong, and R. Bulla, “Quantum phase transitions in the sub-Ohmic spin-boson model: Failure of the
quantum-classical mapping,” Phys. Rev. Lett. 94, 070604 (2005).
[12] J. A. Hoyos and T. Vojta, “Theory of smeared quantum phase transitions,” Phys. Rev. Lett. 100, 240601 (2008).
[13] J. A. Hoyos and T. Vojta, “Dissipation effects in random transverse-field Ising chains,” Phys. Rev. B 85, 174403 (2012).
[14] S. Sinha and S. Dattagupta, “Model study of dissipation in quantum phase transitions,” Euro. Phys. J. B 86, 96 (2013).
[15] S. Chakravarty and J. Rudnick, “Dissipative dynamics of a two-state system, the Kondo problem, and the inverse-square
Ising model,” Phys. Rev. Lett. 75, 501 (1995).
[16] P. Werner, K. V ̈olker, M. Troyer, and S. Chakravarty, “Phase diagram and critical exponents of a dissipative Ising spin
chain in a transverse magnetic field,” Phys. Rev. Lett. 94, 047201 (2005).
[17] M. H. S. Amin, P. J. Love, and C. J. S. Truncik, “Thermally assisted adiabatic quantum computation,”
Phys. Rev. Lett. 100, 060503 (2008).
[18] T. Albash and D. A. Lidar, “Decoherence in adiabatic quantum computation,” Phys. Rev. A 91, 062320 (2015).
[19] P. Werner, M. Troyer, and S. Sachdev, “Quantum spin chains with site dissipation,” J. Phys. Soc. Jpn. 74, 67 (2005).
[20]P. Werner and M. Troyer, “Cluster Monte Carlo algorithms for dissipative quantum systems,”
Prog. Theor. Phys. Suppl. 160, 395 (2005).
[21] I. B. Sperstad, E. B. Stiansen, and A. Sudbø, “Monte Carlo simulations of dissipative quantum Ising models,”
Phys. Rev. B 81, 104302 (2010).
[22] S. Pankov, S. Florens, A. Georges, G. Kotliar, and S. Sachdev, “Non-Fermi-liquid behavior from two-dimensional antifer-
romagnetic fluctuations: A renormalization-group and large-N analysis,” Phys. Rev. B 69, 054426 (2004).
[23] S. Sachdev, P. Werner, and M. Troyer, “Universal conductance of nanowires near the superconductor-metal quantum
transition,” Phys. Rev. Lett. 92, 237003 (2004).
[24] G. E. Santoro and E. Tosatti, “Optimization using quantum mechanics: quantum annealing through adiabatic evolution,”
J. Phys. A: Math. Gen. 39, R393 (2006).
[25] A. Das and B. Chakrabarti, “Quantum annealing and analog quantum computation,” Rev. Mod. Phys. 80, 1061 (2008).
[26] H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena (Oxford University Press, Oxford,
United Kingdom, 2011).
[27] H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, International series of monographs on physics
(Oxford University Press, Oxford, United Kingdom, 1971).
[28] G. S. Joyce, “Spherical model with long-range ferromagnetic interactions,” Phys. Rev. 146, 349 (1966).
[29] T. K. Kope ́c and R. Pirc, “Quantum spherical description of an Ising spin glass in a transverse field,”
Phys. Rev. B 55, 5623 (1997).
[30] T. Kadowaki and H. Nishimori, “Quantum annealing in the transverse Ising model,” Phys. Rev. E 58, 5355 (1998).
[31] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, “A quantum adiabatic evolution algorithm
applied to random instances of an NP-complete problem.” Science 292, 472 (2001).
[32] M. Suzuki, “Relationship between d-dimensional quantal spin systems and (d + 1)-dimensional Ising systems,”
Prog. Theor. Phys. 56, 1454 (1976).
[33] A. Altland and B. Simons, Condensed Matter Field Theory, 2nd ed. (Cambridge University Press, Cambridge, United
Kingdom, 2010).
[34] V. J. Emery and A. Luther, “Low-temperature properties of the Kondo Hamiltonian,” Phys. Rev. B 9, 215 (1974).
[35] P. Werner and M. Troyer, “Effective charging energy of the single-electron box,”
J. Stat. Mech.: Theor. Exp. 2005, P01003 (2005).
[36] T. H. Berlin and M. Kac, “The spherical model of a ferromagnet,” Phys. Rev. 86, 821 (1952).
[37] H. E. Stanley, “Spherical model as the limit of infinite spin dimensionality,” Phys. Rev. 176, 718 (1968).
[38] A. Pelissetto and E. Vicari, “Critical phenomena and renormalization-group theory,” Phys. Rep. 368, 549 (2002).
[39] S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, United Kingdom, 1999).
[40] “NIST Digital Library of Mathematical Functions: 7.12,” http://dlmf.nist.gov/7.12, Release 1.0.10 of 2015-08-07.

14

Mean Field Analysis of Quantum Annealing Correction
Shunji Matsuura, Hidetoshi Nishimori, Tameem Albash, Daniel A. Lidar
(Submitted on 26 Oct 2015 (v1), last revised 3 Jun 2016 (this version, v2))
https://arxiv.org/abs/1510.07709
Phys. Rev. Lett. 116, 220501 (2016)

[1] A. M. Childs and W. van Dam, Reviews of Modern Physics 82, 1 (2010).
[2] S. Jordan, “Quantum algorithm zoo,” .
[3] H.-P. Breuer and F. Petruccione, The Theory of Open
Quantum Systems (Oxford University Press, 2002).
[4] D. Lidar and T. Brun, eds., Quantum Error Correction
(Cambridge University Press, Cambridge, UK, 2013).
[5] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355
(1998).
[6] P. Ray, B. K. Chakrabarti, and A. Chakrabarti, Phys.
Rev. B 39, 11828 (1989).
[7] J. Brooke, D. Bitko, T. F., Rosenbaum, and G. Aeppli,
Science 284, 779 (1999).
[8] J. Brooke, T. F. Rosenbaum, and G. Aeppli, Nature
413, 610 (2001).
[9] G. E. Santoro, R. Martonˇa ́k, E. Tosatti, and R. Car,
Science 295, 2427 (2002).
[10] W. M. Kaminsky, S. Lloyd, and T. P. Orlando, “Quan-
tum computing and quantum bits in mesoscopic sys- tems,” (Springer, New York, 2004) Chap. 25, pp. 229– 236.
[11] E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, arXiv:quant-ph/0001106 (2000).
[12] D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, SIAM J. Comput. 37, 166 (2007).
[13] A. Mizel, D. A. Lidar, and M. Mitchell, Phys. Rev. Lett. 99, 070502 (2007).
[14] D. Gosset, B. M. Terhal, and A. Vershynina, Physical Review Letters 114, 140501 (2015).
[15] S. Lloyd and B. Terhal, arXiv:1509.01278 (2015).
[16] M. W. Johnson, P. Bunyk, F. Maibaum, E. Tolkacheva, A. J. Berkley, E. M. Chapple, R. Harris, J. Johansson, T. Lanting, I. Perminov, E. Ladizinsky, T. Oh, and G. Rose, Superconductor Science and Technology 23,
065004 (2010).
[17] A. J. Berkley, M. W. Johnson, P. Bunyk, R. Harris,
J. Johansson, T. Lanting, E. Ladizinsky, E. Tolkacheva, M. H. S. Amin, and G. Rose, Superconductor Science and Technology 23, 105014 (2010).
[18] R. Harris, M. W. Johnson, T. Lanting, A. J. Berkley, J. Johansson, P. Bunyk, E. Tolkacheva, E. Ladizinsky, N. Ladizinsky, T. Oh, F. Cioata, I. Perminov, P. Spear, C. Enderud, C. Rich, S. Uchaikin, M. C. Thom, E. M. Chapple, J. Wang, B. Wilson, M. H. S. Amin, N. Dickson, K. Karimi, B. Macready, C. J. S. Truncik, and G. Rose, Phys. Rev. B 82, 024511 (2010).
[19] P. I. Bunyk, E. M. Hoskinson, M. W. Johnson, E. Tolka- cheva, F. Altomare, A. Berkley, R. Harris, J. P. Hilton, T. Lanting, A. Przybysz, and J. Whittaker, Applied Su- perconductivity, IEEE Transactions on, Applied Super-
conductivity, IEEE Transactions on 24, 1 (Aug. 2014).
[20] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lund- gren, and D. Preda, Science 292, 472 (2001).
[21] A. Lucas, Front. Phys. 2, 5 (2014).
[22] T. F. Rønnow, Z. Wang, J. Job, S. Boixo, S. V. Isakov, D. Wecker, J. M. Martinis, D. A. Lidar, and M. Troyer, Science 345, 420 (2014).
[23] S. Aaronson, Nat Phys 11, 291 (2015).
[24] A. M. Childs, E. Farhi, and J. Preskill, Phys. Rev. A 65, 012322 (2001).
[25] M. S. Sarandy and D. A. Lidar, Phys. Rev. Lett. 95, 250503 (2005).
[26] J. Aberg, D. Kult, and E. Sjo ̈qvist, Physical Review A 72, 042317 (2005).
[27] J. Roland and N. J. Cerf, Phys. Rev. A 71, 032330 (2005).
[28] T. Albash and D. A. Lidar, Physical Review A 91, 062320 (2015).
[29] K. C. Young, M. Sarovar, and R. Blume-Kohout, Phys. Rev. X 3, 041013 (2013).
[30] J. Preskill, Quant. Inf. Comput. 13, 181 (2013).
[31] S. P. Jordan, E. Farhi, and P. W. Shor, Phys. Rev. A 974, 052322 (2006).
[32] D. A. Lidar, Phys. Rev. Lett. 100, 160506 (2008).
[33] G. Quiroz and D. A. Lidar, Phys. Rev. A 86, 042333 (2012).
[34] K. C. Young, R. Blume-Kohout, and D. A. Lidar, Phys. Rev. A 88, 062314 (2013).
[35] A. Ganti, U. Onunkwo, and K. Young, Phys. Rev. A 89, 042313 (2014).
[36] A. Mizel, arXiv:1403.7694 (2014).
[37] K. L. Pudenz, T. Albash, and D. A. Lidar, Nat. Comun. 5, 3243 (2014).
[38] K. L. Pudenz, T. Albash, and D. A. Lidar, Phys. Rev. A 91, 042302 (2015).
[39] W. Vinci, T. Albash, G. Paz-Silva, I. Hen, and D. A. Lidar, arXiv:1507.02658 (2015).
[40] A. Mishra, T. Albash, and D. Lidar, arXiv:1508.02785 (2015).
[41] D. Venturelli, S. Mandra`, S. Knysh, B. O’Gorman, R. Biswas, and V. Smelyanskiy, arXiv:1406.7553 (2014).
[42] A. D. King and C. C. McGeoch, arXiv:1410.2628 (2014).
[43] A. Perdomo-Ortiz, J. Fluegemann, R. Biswas, and V. N. Smelyanskiy, arXiv:1503.01083 (2015).
[44] D. Gottesman, Phys. Rev. A 54, 1862 (1996).
[45] L. Chayes, N. Crawford, D. Ioffe, and A. Levit, Journal of Statistical Physics 133, 131 (2008).
[46] F. Krzakala, A. Rosso, G. Semerjian, and F. Zamponi, Phys. Rev. B 78, 134428 (2008).
[47] T. Jo ̈rg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pujos, EPL (Europhysics Letters) 89, 40004 (2010).
[48] S. Suzuki, J. Inoue, and B. Chakrabarti, Quantum Ising Phases and Transitions in Transverse Ising Models, 2nd ed., Lecture Notes in Physics, Vol. 862 (Springer Verlag, Berlin, 2013).
[49] J. Hubbard, Physical Review Letters 3, 77 (1959).
[50] M. Filippone, S. Dusuel, and J. Vidal, Phys. Rev. A 83, 022327 (2011).
[51] E. Farhi, J. Goldstone, and S. Gutmann, arXiv:quant- ph/0208135 (2002).
[52] A. Boulatov and V. N. Smelyanskiy, Phys. Rev. A 68, 062321 (2003).
[53] Y. Seki and H. Nishimori, Phys. Rev. E 85, 051112 (2012).
[54] H. Nishimori and Y. Nonomura, Journal of the Physical
Society of Japan 65, 3780 (1996).
[55] Y. Seki and H. Nishimori, Journal of Physics A: Mathe-
matical and Theoretical 48, 335301 (2015).
[56] H. Nishimori, Statistical Physics of Spin Glasses and In- formation Processing: An Introduction (Oxford Univer-
sity Press, Oxford, UK, 2001).
[57] B. Seoane and H. Nishimori, Journal of Physics A: Math-
ematical and Theoretical 45, 435301 (2012).
[58] A. J. Bray and M. A. Moore, Journal of Physics C: Solid
State Physics 13, L655 (1980).
[59] The initial state is |+⟩···|+⟩. To see that it belongs to
the {|J = N , M⟩} subspace note that, e.g., for N = 2, 2
spanned by |J = 1,M = −1,0,1⟩ = {|00⟩, 1 (|01⟩ + 2
|10⟩), |11⟩}.
[60] L. Mandel and E. Wolf, Optical Coherence and Quantum
Optics (Cambridge University Press, New York, 1995). [61] D. J. Amit, H. Gutfreund, and H. Sompolinsky, Annals
of Physics 173, 30 (1987).

15

Anomalous behavior of the energy gap in the one-dimensional quantum XY model
Manaka Okuyama, Yuuki Yamanaka, Hidetoshi Nishimori, Marek M. Rams
(Submitted on 12 Aug 2015)
https://arxiv.org/abs/1508.02814
Phys. Rev. E 92, 052116 (2015)

[1] H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena, (Oxford, 2011).
[2] R. R. dos Santos and R. B. Stinchcombe, J. Phys. A: Math. Gen. 14, 2741 (1981).
[3] A. Osterloh, Luigi Amico, G. Falci, and Rosario Fazio, Nature 416, 608 (2002).
[4] V. Privman and M. E. Fisher, J. Stat. Phys. 33, 385 (1983).
[5] N. Hatano, Y. Nishiyama and M. Suzuki, J. Phys. A: Math. Gen. 27, 6077 (1994).
[6] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[7] T. Kadowaki, Thesis, Tokyo Institute of Technology (1998); arXiv:quant-ph/0205020.
[8] A. B. Finilla, M.A. Gomez, C. Sebenik, and D. J. Doll, Chem. Phys. Lett. 219, 343 (1994).
[9] S. Morita and H. Nishimori, J. Math. Phys. 49, 125210 (2008).
[10] A. Das and B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
[11] G. E. Santoro and E. Tosatti, J. Phys. A: Math. Gen. 39, R292 (2006).
[12] V. Bapst, L. Foini, F. Krzakala, G. Semerjian, and F. Zamponi, Phys. Rep. 523, 127 (2013).
[13] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, and D. Preda, Science 292, 474 (2001).
[14] Y. Seki and H. Nishimori, Phys. Rev. E 85, 051112 (2012).
[15] B. Seoane and H. Nishimori, J. Phys. A: Math. Theor. 45, 435301 (2012).
[16] V. Bapst and G. Semerjian, J. Stat. Mech. 2012, P06007 (2012).
[17] T. Jo ̈rg, F. Krzakala, J. Kurchan, A. C. Maggs, and P. Pujos, EPL 89, 40004 (2010).
[18] A. P. Young, S. Knysh, and V. N. Smelyanskiy, Phys. Rev. Lett. 104, 020502 (2010).
[19] A. P. Young, S. Knysh, and V. N. Smelyanskiy, Comp. Phys. Commun. 182, 27 (2011).
[20] G. G. Cabrera and R. Jullien, Phy. Rev. Lett. 57, 393 (1986).
[21] G. G. Cabrera and R. Jullien, Phys. Rev. B 35, 7062 (1987).
[22] C. R. Laumann, R. Moessner, A. Scardicchio, and S. L. Sondhi, Phys. Rev. Lett. 109, 030502
(2012).
[23] J. Tsuda, Y. Yamanaka, H. Nishimori, J. Phys. Soc. Jpn. 82, 114004 (2013).
[24] M. Henkel, J. Phys. A 20, 995 (1987).
[25] S. Sachdev, Quantum Phase Transitions (Cambridge : Cambridge University Press), (2011).
[26] B. Damski and M. M. Rams, J. Phys. A: Math. Theor. 47, 025303 (2014).
[27] E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. 16, 407 (1961).
[28] S. Katsura, Phys. Rev. 127, 1508 (1962).
[29] P. Pfeuty, Ann. Phys. 57, 79 (1970).
[30] E. Barouch and B. M. McCoy, Phys. Rev. A 3, 786 (1971).
[31] J. Kurmann, H. Thomas, and G. Mu ̈ller, Physica A 112, 235 (1982).
[32] C. Hoeger, G. von Gehlen and V. Rittenberg, J. Phys. A: Math. Gen. 18, 1813 (1985).
[33] M. Kenzelmann, R.Coldea, D. A. Tennant, D. Visser, M. Hofmann, P. Smeibidl, and Z.
Tylczynski, Phys. Rev. B 65, 144432 (2002).
[34] A. De Pasquale and P. Facchi, Phys. Rev. A 80, 032102 (2009).
[35] M. Campostrini and E. Vicari, Phys. Rev. A 81, 063614 (2010).
[36] M. Campostrini, J. Nespolo, A. Pelissetto, and E. Vicari, Phys. Rev. Lett. 113, 070402 (2014).
[37] M. Campostrini, A. Pelissetto, and E. Vicari, Phys. Rev. E 91, 042123 (2015).
[38] B. M. McCoy, Phys. Rev. 173, 531 (1968).
[39] V. Zauner, D. Draxler, L. Vanderstraeten, M. Degroote, J. Haegeman, M. M. Rams., V.
Stojevic, N. Schuch and F.Verstraete, New J. Phys. 17 053002 (2015).

16

Adiabatic approximation for the imaginary-time Schroedinger equation and its application to simulated annealing
Kazuya Kaneko, Hidetoshi Nishimori
(Submitted on 2 Apr 2015 (v1), last revised 6 Aug 2015 (this version, v2))
https://arxiv.org/abs/1504.00425
J. Phys. Soc. Jpn. 84, 094001 (2015)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).
H. Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford
University Press, Oxford, U.K., 2001).
T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
G. E. Santoro and E. Tosatti, J. Phys. A 39, R393 (2006).
A. Das and B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, arXiv:0001106.
R. D. Somma, D. Nagaj, and M. Kieferova ́, Phys. Rev. Lett. 109, 050501 (2012).
C. Henley, J. Phys.: Condens. Matter 16, S891 (2004).
C. Castelnovo, C. Chamon, C. Mudry, and P. Pujol, Ann. Phys. 318, 316 (2005).
R. D. Somma, C. Batista, and G. Ortiz, Phys. Rev. Lett. 99, 030603 (2007).
H. Nishimori, J. Tsuda, and S. Knysh, Phys. Rev. E 91, 012104 (2015).
S. Geman and D. Geman, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 721 (1984).
S. Morita and H. Nishimori, J. Math. Phys. (N.Y.) 49, 125210 (2008).
C. De Grandi, A. Polkovnikov, and A. W. Sandvik, Phys. Rev. B 84, 224303 (2011).
A. Messiah, Quantum Mechanics (Wiley, New York, 1976).
E. Hopf, J. Math. Mech. 12, 683 (1963).

17

Relation of classical non-equilibrium dynamics and quantum annealing
Hidetosni Nishimori
(Submitted on 7 Mar 2015)
https://arxiv.org/abs/1503.02127
Proceedings of STATPHYS-KOLKATA VIII

[1] Kadowaki T and Nishimori H 1998 Phys. Rev. E 58 5355
[2] Santoro G E and Tosatti E 2006 J. Phys. A: Math. Gen. 39 R393
[3] Das A and Chakrabarti B K 2008 Rev. Mod. Phys. 80 1061
[4] Suzuki S, Inoue J -i and Chakrabarti B K 2013 Quantum Ising Phases and Transitions in the Transverse
Ising Models (Heidelberg: Springer), Chapter 8
[5] Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A, and Preda D 2001 Science 292 472 (2001)
[6] Kirkpatrick S, Gelatt Jr C D, and Vecchi M P 1983 Science 220 671
[7] Aarts E and Korst J 1989 Simulated Annealing and Boltzmann Machines (Hoboken, New Jersey: Wiley) [8] Kadowaki T 1998 Thesis, Tokyo Institute of Technology; arXiv:quant-ph/0205020.
[9] Johnson J W et al. 2011 Nature 473 194
[10] Perdomo-Ortiz A, Dickson N, Drew-Brook M, Rose G, and Aspuru-Guzik A 2012 Scientific Reports 2 571 [11] Boixo S, Albash T, Spedalieri F M, N Chancellor and Lidar D 2013 Nature Commun 4 2067
[12] Dickson N G et al. 2013 Nature Commun 4 1903
[13] Bian A, Chudak F, Macready W G, Clark L and Gaitan F 2013 Phys. Rev. Lett. 111 130505
[14] Boixo S et al. 2014 Nature Phys. 10 218
[15] Pudenz K L, Albash T and Lidar D L 2014 Nature Comm. 5 3243
[16] Ronnow T F et al. 2014 Science 345 420
[17] Lanting T et al. 2014 Phys. Rev. X 4 021041
[18] Vinci W, Albash T, Mishra A, Warburton P A and Lidar D A 2014 Preprint arXiv:1403.4228 [19] Katzgraber H G, Hamze F and Andrist R S 2014 Phys. Rev. X 4 021008
[20] Venturelli D, Mandra S and Knysh S 2014 Preprint arXiv:1406.7553
[21] Perdomo-Ortiz A et al. 2014 Preprint arXiv:1406.7601
[22] Boixo S et al. 2014 Preprint arXiv:1411.4036
[23] Pudenz K L, Albash T and Lidar D A 2014 Preprint arXiv:1408.4382
[24] Hen I et al. 2014 Preprint arXiv:1502.01663
[25] Martin-Mayor V and Hen I 2015 Preprint arXiv:1502.02494
[26] Boixo S et al. 2015 Preprint arXiv:1502.05754
[27] Morita S and Nishimori H 2006 J. Phys. A: Math. Gen. 39 13903
[28] Morita S and Nishimori H 2007 J. Phys. Soc. Jpn. 76 064002
[29] Morita S and Nishimori H 2008 J. Math. Phys. 49 125210
[30] Morita S 2008 Thesis, Tokyo Institute of Technology
[31] Nishimori H, Tsuda J and Knysh S 2015 Phys. Rev. E 91 012104
[32] Henley C 2004 J. Phys.: Cond. Matt 16 S891
[33] Castelnovo C, Chamon C, Mudry C and Pujol P 2005 Ann. Phys. 318 316

18

Anomalous behavior of the energy gap in the one-dimensional quantum XY model
Yuuki Yamanaka, Hidetoshi Nishimori
(Submitted on 13 Jan 2015 (v1), last revised 13 Aug 2015 (this version, v2))
https://arxiv.org/abs/1501.02926
This paper has been withdrawn by the author, because a significantly improved version has been uploaded as a new submission, arXiv:1508.02814

19

Quantum Annealing with Antiferromagnetic Transverse Interactions for the Hopfield Model
Yuya Seki, Hidetoshi Nishimori
(Submitted on 2 Oct 2014 (v1), last revised 12 Aug 2015 (this version, v2))
https://arxiv.org/abs/1410.0450

[1] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[2] T. Kadowaki, Thesis, Tokyo Institute of Technology (1998), arXiv:quant-ph/0205020.
[3] A. B. Finnila, M. A. Gomez, C. Sebenik, C. Stenson, and J. D. Doll, Chem. Phys. Lett. 219, 343 (1994).
[4] A. Das and B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
[5] G. E. Santoro and E. Tosatti, J. Phys. A: Math. Gen. 39, R393 (2006).
[6] S. Morita and H. Nishimori, J. Math. Phys. 49, 125210 (2008).
[7] V. Bapst, L. Foini, F. Krzakala, G. Semerjian, and F. Zamponi, Phys. Rep. 523, 127 (2013).
[8] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science 292, 472 (2001).
[9] R. D. Somma, D. Nagaj, and M. Kieferov ́a, Phys. Rev. Lett. 109, 050501 (2012).
[10] A. Messiah, Quantum Mechanics (Dover Publications, Inc., New York, 1999).
[11] T. Jo ̈rg, F. Krzakala, J. Kurchan, and A. C. Maggs, Phys. Rev. Lett. 101, 147204 (2008).
[12] T. Jo ̈rg, F. Krzakala, G. Semerjian, and F. Zamponi, Phys. Rev. Lett. 104, 207206 (2010).
[13] T. Jo ̈rg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pujos, EPL 89, 40004 (2010).
[14] J. Tsuda, Y. Yamanaka, and H. Nishimori, J. Phys. Soc. Japan 82, 114004 (2013).
[15] L. Foini, G. Semerjian, and F. Zamponi, Phys. Rev. Lett. 105, 167204 (2010).
[16] A. P. Young, S. Knysh, and V. N. Smelyanskiy, Phys. Rev. Lett. 104, 020502 (2010).
[17] Y. Seki and H. Nishimori, Phys. Rev. E 85, 051112 (2012).
[18] B. Seoane, and H. Nishimori, J. Phys. A: Math. Theor. 45, 435301 (2012)
[19] J. J. Hopfield, Proc. Natl. Acad. Sci. U.S.A. 79, 2554 (1982).
[20] D. J. Amit, H. Gutfreund, and H. Sompolinsky, Phys. Rev. A 32, 1007 (1985).
[21] D. J. Amit, H. Gutfreund, and H. Sompolinsky, Ann. Phys. 173, 30 (1987).
[22] H. Nishimori and Y. Nonomura, J. Phys. Soc. Japan 65, 3780 (1996).
[23] E. Gardner, J. Phys. A 20, 3453 (1987).
[24] Y. Ma and C. Gong, Phys. Rev. E 51, 1573 (1995).
23
[25] J. Hertz, A. Krogh, and R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Redwood City, 1991).
[26] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976).

20

Comparative Study of the Performance of Quantum Annealing and Simulated Annealing
Hidetoshi Nishimori, Junichi Tsuda, Sergey Knysh
(Submitted on 23 Sep 2014 (v1), last revised 12 Dec 2014 (this version, v2))
https://arxiv.org/abs/1409.6386
Phys. Rev. E 91, 012104 (2015)

[1] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[2] T. Kadowaki, Thesis, Tokyo Institute of Technology (1998), arXiv:quant-ph/0205020.
[3] G. Santoro and E. Tosatti, J. Phys. A: Math. Gen. 39, R393 (2006).
[4] A. Das and B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
[5] S. Suzuki, J.-i. Inoue, and B. K. Chakrabarti, Quantum Ising Phases and Transitions in
Transverse Ising Models (Springer, Heidelberg, 2013), Chap. 8.
[6] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science 292, 472
(2001).
[7] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 4598 (1983).
[8] S. Morita and H. Nishimori, J. Math. Phys. 49, 125210 (2008).
[9] J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli, Science 284, 779 (1999).
[10] M. W. Johnson, M. H. S. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, A. J. Berkley, J. Johansson, P. Bunyk, E. M. Chapple, C. Enderud, J. P. Hilton, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, C. J. S. Truncik, S. Uchaikin, J. Wang, B. Wilson, and G. Rose, Nature 473, 194 (2011).
[11] A. Perdomo-Ortiz, N. Dickson, M. Drew-Brook, G. Rose, and A. Aspuru-Guzik, Scientific Reports 2, 571 (2012).
[12] S. Boixo, T. Albash, F. M. Spedalieri, N. Chancellor, and D. A. Lidar, Nature Commun. 4, 2067 (2013).
[13] N. G. Dickson, M. W. Johnson, . H. Amin, R. Harris, F. Altomare, A. J. Berkley, P. Bunyk, J. Cai, E. M. Chapple, P. Chavez, F. Cioata, T. Cirip, P. DeBuen, M. Drew-Brook, C. Enderud, S. Gildert, F. Hamze, J. P. Hilton, E. Hoskinson, K. Karimi, E. Ladizinsky, M. Ladizinsky, T. Lanting, T. Mahon, R. Neufeld, T. Oh, I. Perminov, C. Petroff, A. Przybysz, C. Rich, P. Spear, A. Tcaciuc, M. C. Thom, E. Tolkacheva, S. Uchaikin, J. Wang, A. B. Wilson, Z. Merali, and G. Rose, Nature Commun. 4, 1903 (2013)
[14] Z. Bian, F. Chudak, W. G. Macready, L. Clark, and F. Gaitan, Phys. Rev. Lett. 111, 130505
(2013).
[15] S. Boixo, T. F. Rønnow, S. V. Isakov, Z. Wang, D. Wecker, D. A. Lidar, J. M. Martinis, and
M. Troyer, Nature Phys. 10 (2014) 218.
[16] K. L. Pudenz, T. Albash and D. A. Lidar, Nature Comm. 5, 3243 (2014).
[17] T. F. Rønnow, Z. Wang, J. Job, S. Boixo, V. Sergei, D. Wecker, J. M. Martinis, and D. A.
Lidar, Science Express 19 June 2014.
[18] T. Lanting, A. J. Przybysz, A. Yu. Smirnov, F. M. Spedalieri, M. H. Amin, A. J. Berkley, R.
Harris, F. Altomare, S. Boixo, P. Bunyk, N. Dickson, C. Enderud, J. P. Hilton, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, R. Neufeld, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, S. Uchaikin, A. B. Wilson, and G. Rose, Phys. Rev. X 4, 021041 (2014).
[19] S. W. Shin, G. Smith, J. A. Smolin, and U. Vazirani, arXiv:1401.7087.
[20] W. Vinci, T. Albash, A. Mishra, P. A. Warburton, and D. A. Lidar, arXiv:1403.4228.
[21] H. G. Katzgraber, F. Hamze, and R. S. Andrist, Phys. Rev. X 4 021008 (2014).
[22] D. Venturelli, S. Mandra, and S. Knysh, arXiv:1406.7553.
[23] A. Perdomo-Ortiz, J. Fluegemann, S. Narasimhan, R. Biswas, and V. N. Smelyanskiy,
arXiv:1406.7601.
[24] T. Albash, T. F. Rønnow, M. Troyer, and D.A. Lidar, arXiv:1409.3827.
[25] R. P. Feynman, Statistical Mechanics, (Westview, 1998).
[26] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976).
[27] C. Henley, J. Phys.: Cond. Matt. 16, S891 (2004).
[28] C. Castelnovo, C. Chamon, C. Mudry, and P. Pujol, Ann. Phys. 318, 316 (2005).
[29] R. D. Somma, C. D. Batista, and G. Ortiz, Phys. Rev. Lett. 99, 030603 (2007).
[30] S. Geman and D. Geman, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 721 (1984).
[31] S. Boixo, G. Ortiz, and R. Somma, arXiv:1409.2477.
[32] A. Das and B. K. Chakrabarti, Phys. Rev. E 78, 061121 (2008).
[33] R. Glauber, J. Math. Phys. 4, 294 (1963).
[34] Y. Seki and H. Nishimori, Phys. Rev. E 85, 051112 (2012).
[35] B. Seoane and H. Nishimori, J. Phys. A: Math. Theor. 45, 435301 (2012).

21

Mean-field theory is exact for the random-field model with long-range interactions
Junichi Tsuda, Hidetoshi Nishimori
(Submitted on 7 Feb 2014 (v1), last revised 10 Jun 2014 (this version, v2))
https://arxiv.org/abs/1402.1581
J. Phys. Soc. Jpn

W. Thirring: Z. Phys. A 235, 339 (1970).
P. Hertel and W. Thirring: Ann. Phys. 63, 520 (1971).
R. S. Ellis, K. Haven, and B. Turkington: J. Stat. Phys. 101, 999 (2000).
J. Barre ́, D. Mukamel, and S. Ruffo: Phys. Rev. Lett. 87, 030601 (2001).
F. Leyvraz and S. Ruffo: J. Phys. A: Math. Gen. 35, 285 (2002).
F. Bouchet and J. Barre ́: J. Stat. Phys. 118, 1073 (2005).
A. Campa, T. Dauxois, and S. Ruffo: Phys. Rep. 480, 57 (2009).
D. Lynden-Bell and R. Wood: Mon. Not. R. Astr. Soc. 138, 495 (1968).
S. A. Cannas, A. C. N. de Magalhaes, and F. A. Tamarit: Phys Rev. B 61, 11521 (2000).
F. Tamarit and C. Anteneodo: Phys. Rev. Lett. 84, 208 (2000).
J. Barre ́: Physica A 305, 172 (2002).
J. Barre ́, F. Bouchet,T. Dauxois, and S.Ruffo: J. Stat. Phys. 119, 677 (2005).
A. Campa, A. Giansanti, and D. Moroni: Phys. Rev. E 62, 303 (2000).
A. Campa, A. Giansanti, and D. Moroni: J. Phys. A: Math. Theor. 36, 6897 (2003).
T. Mori: Phys. Rev. E 84, 031128 (2011).
T. Mori: Phys. Rev. E 82, 060103 (2010).
T. Mori: J. Stat. Mech. 2013, P10003 (2013).
The random-field Ising model with power-law interactions has also been discussed when the power is large and the system behaves effectively like a model with short-range interactions. See L. Leuzzi and G. Parisi, Phys. Rev. B 88, 224204 (2013), T. Dewenter and A. K. Hartmann, arXiv:1307.3987 and references cited therein.
Z. Bertalan, T. Kuma, Y. Matsuda and H. Nishimori: J. Stat. Mech. 2011, P01016 (2011).

22

Energy gap at first-order quantum phase transitions: An anomalous case
Junichi Tsuda, Yuuki Yamanaka, Hidetoshi Nishimori
(Submitted on 10 Jun 2013 (v1), last revised 6 Sep 2013 (this version, v2))
https://arxiv.org/abs/1306.2142
J. Phys. Soc. Jpn. 82 (2013) 114004

T. Kadowaki and H. Nishimori: Phys. Rev. E 58 (1998) 5355.
S. Morita and H. Nishimori: J. Math. Phys. 49 (2008) 125210.
A. B. Finilla, M. A. Gomez, C. Sebenik, and D. J. Doll: Chem. Phys. Lett. 219 (1994) 343.
A. Das and B. K. Chakrabarti: Rev. Mod. Phys. 80 (2008) 1061.
G. E. Santoro and E. Tosatti: J. Phys. A: Math. Theor. 39 (2006) R393.
S. Suzuki, J.-i. Inoue, and B. K. Chakrabarti: Quantum Ising Phases and Transitions in Transverse Ising Models (Springer, Heidelberg, 2012).
E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda: Science 292 (2001) 474.
Y. Seki and H. Nishimori: Phys. Rev. E 85 (2012) 051112.
B. Seoane and H. Nishimori: J. Phys. A: Math. Theor. 45 (2012) 435301.
V. Bapst and G. Semerjian: J. Stat. Mech. (2012) P06007.
T. Jo ̈rg, F. Krzakala, J. Kurchan, A. C. Maggs, and P. Pujos: EPL 89 (2010) 40004.
G. Cabrera and R. Jullien: Phys. Rev. B 35 (1987) 7061.
C. R. Laumann, R. Moessnner, A. Scardicchio, and S. L. Sondhi: Phys. Rev. Lett. 109 (2012) 030502.
H. J. Lipkin, N. Meshkov, and A. J. Glick: Nucl. Phys. 62 (1965) 188.
R. Botet and R. Jullien: Phys. Rev. B 28 (1983) 3955.
S. Dusuel and J. Vidal: Phys. Rev. B 71 (2005) 224420.
M. Filippone, S. Dusuel and J. Vidal: Phys. Rev. A 83 (2011) 022327.
Note that the gap ∆(Γ, h) discussed in the previous section is the limit of ∆N (Γ, h) as N → ∞.
In the strict absence of a longitudinal field h = 0, the even-odd parity of M is conserved and thus the proper gap is the one between the ground state and the second excited state. However, since we are interested in quantum annealing driven by the longitudinal field, which changes the parity of M, it is legitimate to study the gap defined here.
In some cases, δ may remain exactly 1/2 for a carefully chosen sequence of N. However, this does not represent the asymptotic behavior we are interested in.
Note that Γ defined by Eq. (22) is irrational because the corresponding δ in Eq. (24) assumes infinitely many values as a function of Nn.
It is at our disposal to choose an appropriate sequence of system size in the realization of quantum annealing, numerical or experimental.

23

Nonadiabatic Quantum Annealing for One-Dimensional Trasverse-Field Ising Model
Hitoshi Katsuda, Hidetoshi Nishimori
(Submitted on 25 Mar 2013)
https://arxiv.org/abs/1303.6045
Phys. Rev. E

[1] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[2] A. B. Finnila, M. A. Gomez, C. Sebenik, C. Stenson, and J. D. Doll, Chem. Phys. Lett. 219,
343 (1994).
[3] A. Das and B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
[4] G. Santoro and E. Tosatti, J. Phys. A. 39, R393 (2006).
[5] S. Morita and H. Nishimori, J. Math. Phys. 49, 125210 (2008).
[6] E. Fahri, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren and D. Preda, Science 292, 472
(2001).
[7] S. Suzuki, J. -i. Inoue and B. K. Chakrabarti, Quantum Ising Phases and Transitions in
Transverse Ising Models, 2nd Edition, Springer, Heidelberg (2013).
[8] V. Bapst, L. Foini, F. Krzakara, G. Semerjian and F. Zamponi, Phys. Rep. 523, 127 (2013).
[9] F. R. Tersenghi, M. Weigt and R. Zecchina, Phys. Rev. E, 63, 026702 (2001).
[10] M. M ́ezard , G. Parisi and M. A. Virasoro, Spin Glass Theory and Beyond, World Scientific, Singapore, (1987).
[11] H. Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction, Oxford University Press, Oxford, U.K. (2001).
[12] A. Messiah, Quantum Mechanics, Vol. 2, North-Holland, Amsterdam (1962).
[13] M. Garey and D. S. Johnson, Computers and Intractability. A Guide to the Theory of NP-
Completeness, W. H. Freeman and Co., San Francisco, (1979).
[14] M. W. Johnson, M. H. S. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, A.
J. Berkley, J. Johansson, P. Bunyk, E. M. Chapple, C. Enderud, J. P. Hilton, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, C. J. S. Truncik, S. Uchaikin, J. Wang, B. Wilson and G. Rose, Nature, 473, 194 (2011).
[15] A. Perdomo-Ortiz, N. Dickson, M. Drew-Brook, G. Rose and A. Aspuru-Guzik, Scientific Reports 2, 571 (2012).
[16] J. Dziarmaga, Phys. Rev. Lett. 95, 245701 (2005).
[17] J. Dziarmaga, Phys. Rev. B. 74, 064416 (2006).
[18] N. V. Vitanov and B. M. Garraway, Phys. Rev. A, 53, 4288 (1996).
8
[19] L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, 2nd ed, Pergamon Press, Oxford (1965).
[20] C. Zener, Proc. Roy. Soc. London Ser. A 137, 696 (1932)

24

Real-space renormalization-group approach to the random transverse-field Ising model in finite dimensions
Ryoji Miyazaki, Hidetoshi Nishimori
(Submitted on 18 Oct 2012 (v1), last revised 14 Jun 2013 (this version, v2))
https://arxiv.org/abs/1210.5053
Phys. Rev. E 87, 032154 (2013)

[1] B. M. McCoy and T. T. Wu, Phys. Rev. 176, 631 (1968).
[2] D. S. Fisher, Phys. Rev. Lett. 69, 534 (1992); Phys. Rev.
B 51, 6411 (1995).
[3] D. S. Fisher, Physica A 263, 222 (1999).
[4] F. Iglo ́i and C. Monthus, Phys. Rep. 412, 277 (2005).
[5] O. Motrunich, S.-C. Mau, D. A. Huse, and D. S. Fisher,
Phys. Rev. B 61, 1160 (2000).
[6] Y.-C. Lin, N, Kawashima, F. Iglo ́i, and H. Rieger, Prog.
Theor. Phys. Suppl. 138, 479 (2000).
[7] D. Karevski, Y.-C. Lin, H. Rieger, N. Kawashima, and
F. Iglo ́i, Eur. Phys. J. B 20, 267 (2001).
[8] I. A. Kova ́cs and F. Iglo ́i, Phys. Rev. B 80, 214416 (2009).
[9] I. A. Kova ́cs and F. Iglo ́i, Phys. Rev. B 82, 054437 (2010). [10] I. A. Kova ́cs and F. Iglo ́i, Phys. Rev. B 83, 174207 (2011). [11] I. A. Kova ́cs and F. Iglo ́i, J. Phys.: Condens. Matter 23,
404204 (2011).
[12] O. Dimitrova and M. M ́ezard, J. Stat. Mech. (2011)
P01020.
[13] M. Guo, R. N. Bhatt, and D. A. Huse, Phys. Rev. Lett.
72, 4137 (1994).
[14] H. Rieger and A. P. Young, Phys. Rev. Lett. 72, 4141
(1994).
[15] R. Miyazaki, H. Nishimori, and G. Ortiz, Phys. Rev. E 83, 051103 (2011).
[16] K. Uzelac, R. Jullien, and P. Pfeuty, J. Phys. A: Math. Gen. 13, 3735 (1980).
[17] P. Pfeuty, Phys. Lett. 72A, 245 (1979).
[18] H. Nishimori and G. Ortiz, Elements of Phase Transi-
tions and Critical Phenomena (Oxford University Press,
Oxford, 2011).
[19] R. Shankar and G. Murthy, Phys. Rev. B 36, 536 (1987).
[20] J. T. Chayes, L. Chayes, D. S. Fisher, and T. Spencer,
Phys. Rev. Lett. 57, 2999 (1986); Commun. Math. Phys. 120, 501 (1989).
[21] A. Fernandez-Pacheco, Phys. Rev. D 19, 3173 (1979). [22] S. D. Drell, M. Weinstein, and S. Yankielowicz, Phys.
Rev. D 16, 1769 (1977).
[23] R. Jullien, P. Pfeuty, J. N. Fields, and S. Doniach, Phys.
Rev. B 18, 3568 (1978).
[24] G. Um, Phys. Rev. B 15, 2736 (1977).
[25] J. E. Hirsch and G. F. Mazenko, Phys. Rev. B 19, 2656
(1979).
[26] B. Hu, Phys. Lett. 71A, 83 (1979).
[27] E. Fradkin and S. Raby, Phys. Rev. D 20, 2566 (1979). [28] F. D. Nobre, Phys. Rev. E 64, 046108 (2001).
[29] C. Pich, A. P. Young, H. Rieger, and N. Kawashima,
Phys. Rev. Lett. 81, 5916 (1998).

25

Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions
Yuma Murata, Hidetoshi Nishimori
(Submitted on 20 Jul 2012 (v1), last revised 2 Nov 2012 (this version, v2))
https://arxiv.org/abs/1207.4887
J. Phys. Soc. Jpn. 81(2012)114008

L. D. Landau and E. M. Lifshitz: Statistical Physics (Butterworth-Heinemann, Oxford, 1984).
R. S. Ellis, H. Touchette and B. Turkington: Physica A 335 (2004) 518.
H. Touchette, R. S. Ellis and B. Turkington: Physica A 340 (2004) 138.
F. Bouchet and J. Barre ́: J. Stat. Phys. 118 (2005) 1073.
A. Campa, T. Dauxois and S. Ruffo: Phys. Rep. 480 (2009) 57.
T. Dauxois, S. Ruffo and E. Arimondo: Dynamics and Thermodynamics of systems with Long-Range Interactions, Lecture Notes in Physics, ed. M. Wilkens (Springer, New York, 2002) Vol. 602.
D. Mukamel:Statistical mechanics of Systems with long-range interactions, in Dynam- ics and Thermodynamics of Systems with Long-Range Interactions: Theory and Exper- iment, eds. A. Campa, A. Giansati, G. Morgi and F.S. Labini (AIP Conference Series, 2008) Vol. 970.
T. Dauxois and S. Ruffo: Les Houches: Summer School 2008, Long-Range Interacting Systems, ed. L. Cugliandolo (Oxford University Press, Oxford, 2009) Vol. 90.
D. Lynden-Bell and R. Wood: Mot. Not. Roy. Astr. Soc. 138 (1968) 495.
D. Lynden-Bell: Physica A 264 (1999) 293.
P. H. Chavanis: Int. J. Mod. Phys. Lett. 87 (2006) 3113.
P. Hertel and W. Thirring: Ann. Phys. 63 (1971) 520.
J. Barre ́, D. Mukamel and S. Ruffo: Phys. Rev. Lett. 87 (2001) 030601.
F. Leyvraz and S. Ruffo: J. Phys. A 35 (2002) 285.
J. Barre ́, F. Bouchet, T Dauxois and S. Ruffo: J. Stat. Phys. 119 (2005) 677.
D. Mukamel, S. Ruffo and N. Schreiber: Phys. Rev. Lett. 95 (2005) 240604.
K. Takahashi, H. Nishimori and V. Martin-Mayor: J. Stat. Mech. (2011) P08024.
A. Lederhendler and D. Mukamel: Phys. Rev. Lett. 105 (2010) 150602.
A. Lederhendler, O. Cohen and D. Mukamel: J. Stat. Mech. (2010) P11016.
H. Nishimori: J. Phys. Soc. Jpn. 80 (2011) 023002.
Z. Bertalan, T. Kuma, Y. Matsuda and H. Nishimori: J. Stat. Mech. (2011) P01016.
Z. Bertalan and K. Takahashi: J. Stat. Mech. (2011) P11022.
Z. Bertalan and H. Nishimori: Phil. Mag. 92 (2012) 2.
J. M. Kosterlitz, D. J. Thouless and R. C. Jones: Phys. Rev. Lett. 36 (1976) 1217.
J. R. L de Almeida, R. C. Jones, J. M. Kosterlitz and D. J. Thouless: J. Phys. C: Solid State Phys. 11 (1978) 871.
I. Ispolatov and E. G. D. Cohen: Physica A 295 (2001) 475.
H. W. J. Blo ̈te, W. Guo and H. J. Hihorst: Phys. Rev. Lett. 88 (2002) 047203.
S. Caracciolo and A. Pelissetto: Phys. Rev. E 66 (2002) 016120.
A. C. D. van Enter and S. B. Shlosman: J. Math. Phys. 255 (2005) 21.
M. L. Mehta: Random Matrices (Academic Press, Boston, 1991).
K. E. Bassler P.J. Forrester, and N. E. Frankel: J. Math. Phys. 50 (2009) 1.

26

Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
Beatriz Seoane, Hidetoshi Nishimori
https://arxiv.org/abs/1207.2909
(Submitted on 12 Jul 2012 (v1), last revised 10 Oct 2012 (this version, v3))
J. Phys. A: Math. Theor. 45 435301 (2012)

[1] Papadimitriou C H and Steiglitz K 1998 Combinatorial Optimization: Algorithms and Complexity (New York: Dover)
[2] Garey M R and Johnson D S 1979 Computers and Intractability (San Francisco: Freeman)
[3] M ́ezard M, Parisi G and Virasoro M 1987 Spin-Glass Theory and Beyond (Singapore: World
Scientific)
[4] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction
(Oxford: Oxford University Press)
[5] Barahona F 1982 J. Phys. A: Math Gen. 15 3241
[6] Hukushima K and Nemoto K 1996 J. Phys. Soc. Jpn. 65 1604
[7] Kirkpatrick S, Gelatt C D J and Vecchi M P 1983 Science 220 671 [8] Kadowaki T and Nishimori H 1998 Phys. Rev. E 58 5355
[9] Finnila A B, Gomez M A, Sebenik C, Stenson C and Doll J D 1994 Chem. Phys. Lett. 219 343 [10] Das A and Chakrabarti B K 2008 Rev. Mod. Phys. 80 1061
[11] Santoro G E and Tosatti E 2006 J. Phys. A 39 R393
[12] Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A and Preda D 2001 Science 292 474 [13] Hogg T 2003 Phys. Rev. A 67 022314
[14] Young A P, Knysh S and Smelyanskiy V N 2008 Phys. Rev. Lett. 101 170503
[15] Young A P and Knysh S 2010 Phys. Rev. Lett. 104 020502
[16] Hen I and Young A P 2011 Phys. Rev. E 84 061152
[17] J ̈org T, Krzakala F, Kurchan J and Maggs A C 2008 Phys. Rev. Lett. 101 147204
[18] J ̈org T, Krazakala F, Kurchan J, Maggs A C and Pujos J 2010 Europhys. Lett. 89 40004 [19] J ̈org T, Krzakala F, Semerjian G and Zamponi F 2010 Phys. Rev. Lett. 104 207206
[20] Seki Y and Nishimori H 2012 Phys. Rev. E 85 051112
[21] Bapst V and Semerjian G 2012 J. Stat. Mech. P06007
[22] Grover L K 1997 Phys. Rev. Lett. 79 325
[23] Roland J and Cerf N J 2003 Phys. Rev. A 68 062312
[24] Grover L K 1996 Proceedings of the 28th Annual Symposium on the Theory of Computing (New
York: ACM Press)
[25] Suzuki M 1976 Prog. Theor. Phys. 56 1454
[26] Filippone M, Dusuel S and Vidal J 2011 Phys. Rev. A 83 022327
[27] Suzuki S, Nishimori H and Suzuki M 2007 Phys. Rev. E 75 051112
[28] den Ouden L, Capel H, Perk J and Tindemans P 1976 Physica A 85 51 [29] den Ouden L, Capel H and Perk J 1976 Physica A 85 425
[30] Perk J, den Ouden L and Capel H 1977 Physica A 89 555

27

Quantum annealing with antiferromagnetic fluctuations
Yuya Seki, Hidetoshi Nishimori
(Submitted on 12 Mar 2012 (v1), last revised 27 Apr 2012 (this version, v2))
https://arxiv.org/abs/1203.2418
Phys. Rev. E 85, 051112 (2012)

[1] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, New York, 1979).
[2] A. K. Hartmann and M. Weigt, Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics (Wiley-VCH, Weinheim, 2005).
[3] J. J. Hopfield and D. W. Tank, Science 233, 625 (1986).
[4] Y. Fu and P. W. Anderson, J. Phys. A 19, 1605 (1986).
[5] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[6] A. B. Finnila, M. A. Gomez, C. Sebenik, C. Stenson, and J. D. Doll, Chem. Phys. Lett. 219,
343 (1994).
18
[7] A. Das and B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
[8] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science 292, 472
(2001).
[9] S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).
[10] S. Morita and H. Nishimori, J. Math. Phys. 49, 125210 (2008).
[11] T. Jo ̈rg, F. Krzakala, J. Kurchan, A. C. Maggs, and J. Pujos, EPL 89, 40004 (2010).
[12] L. K. Grover, Phys. Rev. Lett. 79, 325 (1997).
[13] T. Jo ̈rg, F. Krzakala, J. Kurchan, and A. C. Maggs, Phys. Rev. Lett. 101, 147204 (2008).
[14] A. P. Young, S. Knysh, and V. N. Smelyanskiy, Phys. Rev. Lett. 104, 020502 (2010).
[15] T. Jo ̈rg, F. Krzakala, G. Semerjian, and F. Zamponi, Phys. Rev. Lett. 104, 207206 (2010),
arXiv:0911.3438v2.
[16] E. Farhi, J. Goldstone, and S. Gutmann, arXiv:quant-ph/0208135.
[17] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976).
[18] H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena (Oxford
Univ. Press, Oxford, 2011).
[19] Thereisnoorderparametertocharacterizethisphasetransitioninthesensetheorderparame-
ter is finite in one phase and zero in the other. We nevertheless call it a phase transition because the energy (free energy) is singular at s = 1/3, f′′ (s = 1/3 − 0,0) ̸= f′′ (s = 1/3 + 0,0).
A similar phenomenon is observed within the ferromagnetic phase, a phase transition from a
ferromagnetic phase to another ferromagnetic phase, as will be shown in Sec. IV.
[20] R. Schu ̈tzhold and G. Schaller, Phys. Rev. A 74, 060304 (2006).
[21] It is to be noted that the special point (s, λ) = (1, 0) has a highly degenerate ground state [24],
among which only the state with the maximum total spin S = N/2 is relevant to our purpose: Quantum annealing starts from s = 0 with S = N/2 and preserves the total spin following the Schro ̈dinger equation (2) with [Hˆ(t),Sˆ2] = 0.
[22] E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, arXiv:quant-ph/0001106.
[23] J. Roland and N. J. Cerf, Phys. Rev. A 65, 042308 (2002).
[24] A. K. Chandra, J. Inoue, and B. K. Chakrabarti, Phys. Rev. E 81, 021101 (2010).

28

Ensemble equivalence in spin systems with short-range interactions
Kazutaka Takahashi, Hidetoshi Nishimori, Victor Martin-Mayor
(Submitted on 31 May 2011 (v1), last revised 7 Aug 2011 (this version, v2))
https://arxiv.org/abs/1105.6144
J. Stat. Mech. (2011) P08024

[1] Ruelle D 1963 Helv. Phys. Acta 36 183
[2] Lynden-Bell D and Wood R 1968 Mon. Not. R. Astro. Soc. 138 495
[3] Hertel P and Thirring W 1971 Ann. Phys. 63 520
[4] Lynden-Bell D and Lynden-Bell R M 1977 Mon. Not. R. Astro. Soc. 181 405 [5] Posch A H and Thirring W 2005 Phys. Rev. Lett. 95 251101
[6] Posch A H and Thirring W 2006 Phys. Rev. E 74 051103
[7] Lynden-Bell D and Lynden-Bell R M 2008 Eur. Phys. Lett. 82 43001
[8] Barr ́e J, Mukamel D and Ruffo S 2001 Phys. Rev. Lett. 87 030601
[9] Ispolatov I and Cohen E G D 2001 Physica A 295 475
[10] Bouchet F and Barr ́e J 2005 J. Stat. Phys. 118 1073
[11] Costeniuc M and Ellis R S 2005 J. Math. Phys. 46 063301
[12] Mukamel D, Ruffo S and Schreiber N 2005 Phys. Rev. Lett. 95 240604
[13] Campa A, Giansanti A, Mukamel D and Ruffo S 2006 Physica A 365 120
[14] Rem ́ırez-Herna ́ndez A, Larralde H and Leyvraz F 2008 Phys. Rev. Lett. 100 120601 [15] Rem ́ırez-Herna ́ndez A, Larralde H and Leyvraz F 2008 Phys. Rev. E 78 061133
[16] Bouchet F, Dauxois T, Mukamel D and Ruffo S 2008 Phys. Rev. E 77 011125
[17] Lederhendler A and Mukamel D 2010 Phys. Rev. Lett. 105 150602
[18] Bouchet F, Gupta S and Mukamel D 2010 Physica A 389 4389
[19] Bertalan Z, Kuma T, Matsuda Y and Nishimori H 2011 J. Stat. Mech. P01016
[20] Bertalan Z and Nishimori H 2011 Phil. Mag. (published online)
[21] Campa A, Dauxois T and Ruffo S 2009 Phys. Rep. 480 57
[22] Schmidt M, Kusche R, Hippler T, Donges J, Kronmu ̈ller W, von Issendorff B and Haberland H
2001 Phys. Rev. Lett. 86 1191
[23] Domany E, Schick M and Swendsen R H 1984 Phys. Rev. Lett. 52 1535
[24] Blo ̈te H W J, Guo W and Hilhorst H J 2002 Phys. Rev. Lett. 88 047203
[25] Caracciolo S and Pelissetto A 2002 Phys. Rev. E 66 016120
[26] van Enter A C D and Shlosman S B 2002 Phys. Rev. Lett. 89 285702
[27] van Enter A C D and Shlosman S B 2005 Commun. Math. Phys. 255 21
[28] Mussardo G 2010 Statistical Field Theory (Oxford: Oxford University Press)
[29] Nishimori H and Ortiz G 2011 Elements of Phase Transitions and Critical Phenomena (Oxford:
Oxford University Press)
[30] Behringer H 2005 J. Stat. Mech. P06014
[31] Kastner M 2009 J. Stat. Mech. P12007
[32] Creutz M 1983 Phys. Rev. Lett. 50 1411
[33] Ota S and Ota S B 1994 Pramana 43 129
[34] Barr ́e J and Gon ̧calves B 2007 Physica A 386 212
[35] Kosterlitz J M and Thouless D J 1973 J. Phys. C: Solid State Phys. 6 1181 [36] Sinha S and Roy S K 2010 Phys. Rev. E 81 041120
[37] Martin-Mayor V 2007 Phys. Rev. Lett. 98 137207

29

Nonequilibrium work on spin glasses in longitudinal and transverse fields
Masayuki Ohzeki, Hitoshi Katsuda, Hidetoshi Nishimori
(Submitted on 4 Apr 2011 (v1), last revised 27 May 2011 (this version, v2))
https://arxiv.org/abs/1104.0484
JPSJ

C. Jarzynski: Phys. Rev. Lett. 78 (1997) 2690.
C. Jarzynski: Phys. Rev. E 56 (1997) 5018.
G. E. Crooks: J. Stat. Phys. 90 (1998) 1481.
G. E. Crooks: Phys. Rev. E 60 (1999) 2721.
G. E. Crooks: Phys. Rev. E 61 (2000) 2361.
K. Binder and A. P. Young: Rev. Mod. Phys. 58 (1986) 801.
A. P. Young (ed.): Spin Glasses and Random Fields (World Scientific, Singapore, 1997).
N. Kawashima and H. Rieger: in Frustrated Spin Systems, ed. T. H. Diep (World Scientific, Sin-
gapore, 2004).
M. M ́ezard, G. Parisi and M. A. Virasoro: Spin Glass Theory and Beyond (World Scientific,
Singapore, 1987).
H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169.
H. Nishimori: Statistical Physics of Spin Glasses and Information Processing: An Introduction
(Oxford Univ. Press, Oxford, 2001).
Y. Ozeki: J. Phys. A: Math. Gen. 28 (1995) 3645.
M. Ohzeki and H. Nishimori: J. Phys. Soc. Jpn. 79 (2010) 084003.
R. M. Neal: Statistics and Computing, 11 (2001) 125.
Y. Iba: Trans. Jpn. Soc. Artif. Intel. 16 (2001) 279.
K. Hukushima and Y. Iba: AIP. Conf. Proc. 690 (2003) 200.
S. Kirkpatrick, C. D. Gelett, and M. P. Vecchi: Science 220 (1983) 671.
K. Hukushima and K. Nemoto: J. Phys. Soc. Jpn. 65 (1996) 1604.
T. Kadowaki and H. Nishimori: Phys. Rev. E 58 (1998) 5355.
S. Morita, and H. Nishimori: J. Math. Phys. 49 (2008) 125210.
M. Ohzeki, and H. Nishimori: J. Comp. Theor. Nanoscience 8 (2011) 963.
S. Morita, H. Nishimori and Y. Ozeki: J. Phys. Soc. Jpn. 75 (2006) 014001.
E. Farhi, J. Goldstone, S. Gutomann and M. Sipser: arXiv:0001106
T. J ̈org, F. Krzakala, J. Kurchan, and A. C. Maggs: Phys. Rev. Lett. 101 (2008) 147204.
A. P. Young, S. Knysh, and V. N. Smelyanskiy: Phys. Rev. Lett. 104 (2010) 020502.
H. Tasaki, arXiv:0009244
M. Campisi, P. Talkner and P. Ha ̈nggi: Phys. Rev. Lett. 102 (2009) 210401.
S. Vaikuntanathan and C. Jarzynski: Phys. Rev. Lett. 100 (2008) 190601.
M. Ohzeki: Phys. Rev. Lett. 105 (2010) 050401.

30

Random-field p-spin glass model on regular random graphs
Yoshiki Matsuda, Hidetoshi Nishimori, Lenka Zdeborová, Florent Krzakala
(Submitted on 31 Jan 2011)
https://arxiv.org/abs/1101.5863
J. Phys. A: Math. Theor. 44 (2011) 185002

[1] Edwards S F and Anderson P W 1975 J. Phys. F: Met. Phys. 5 965
[2] Sherrington D and Kirkpatrick S 1975 Phys. Rev. Lett. 35 1792–1796
[3] M ́ezard M, Parisi G and Virasoro M A 1987 Spin Glass Theory and Beyond (Singapore: World
Scientific)
[4] Fischer K H and Hertz J A 1991 Spin Glasses (Cambridge: Cambridge University Press)
[5] Young A P (ed) 1998 Spin Glasses and Random Fields (Singapore: World Scientific)
[6] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction
(Oxford University Press)
[7] M ́ezard M and Montanari A 2009 Information, Physics, and Computation (Oxford University
Press)
[8] de Almeida J R L and Thouless D J 1978 J. Phys. A: Math. Gen. 11 983 [9] Thouless D J 1986 Phys. Rev. Lett. 56 1082–1085
[10] Rivoire O, Biroli G, Martin O C and Mezard M 2004 Eur. Phys. J. B 37 55–78 [11] Martin O C, M ́ezard M and Rivoire O 2005 J. Stat. Mech. 2005 P09006
[12] M ́ezard M and Parisi G 2001 Eur. Phys. J. B 20 217–233
[13] Aharony A 1978 Phys. Rev. B 18 3318–3327
[14] Bruinsma R 1984 Phys. Rev. B 30 289–299
[15] Wohlman O E and Domb C 1984 J. Phys. A: Math. Gen. 17 2247–2256 [16] de Almeida J R L and Bruinsma R 1987 Phys. Rev. B 35 7267–7270 [17] M ́ezard M and Parisi G 1990 J. Phys. A: Math. Gen. 23 L1229
[18] M ́ezard M and Young A 1992 Europhys. Lett. 18 653
[19] M ́ezard M and Monasson R 1994 Phys. Rev. B 50 7199–7202
[20] De Dominicis C, Orland H and Temesvari T 1995 J. Phys. I France 5 987–1001
[21] Br ́ezin E and Dominicis C 1998 Europhys. Lett. 44 13
[22] Br ́ezin E and De Dominicis C 2001 Eur. Phys. J. B 19 467–471
[23] Pastor A A, Dobrosavljevi ́c V and Horbach M L 2002 Phys. Rev. B 66 014413
[24] Krzakala F, Ricci-Tersenghi F and Zdeborov ́a L 2010 Phys. Rev. Lett. 104 207208
[25] Bouchaud J and M ́ezard M 1994 J. Phys. I France 4 1109–1114
[26] Marinari E, Parisi G and Ritort F 1994 J. Phys. A: Math. Gen. 27 7647
[27] Franz S and Hertz J 1995 Phys. Rev. Lett. 74 2114–2117
[28] Franz S, M ́ezard M, Ricci-Tersenghi F, Weigt M and Zecchina R 2001 Europhys. Lett. 55 465 [29] Obuchi T, Kabashima Y and Nishimori H 2009 J. Phys. A: Math. Theor. 42 5004
[30] Matsuda Y, Mu ̈ller M, Nishimori H, Obuchi T and Scardicchio A 2010 J. Phys. A: Math. Theor.
43 285002
[31] Katsura S, Inawashiro S and Fujiki S 1979 Physica A 99 193–216
[32] Nakanishi K 1981 Phys. Rev. B 23 3514–3522
[33] Bowman D R and Levin K 1982 Phys. Rev. B 25 3438–3441
[34] Montanari A, Ricci-Tersenghi F and Semerjian G 2008 J. Stat. Mech. 2008 P04004
[35] Zdeborov ́a L 2009 Acta Physica Slovaca 59 169–303
[36] Pagnani A, Parisi G and Rati ́eville M 2003 Phys. Rev. E 68 046706
[37] Krzakala F 2005 Prog. Theor. Phys. Supp. 77–81
[38] J ̈org T, Katzgraber H G and Krzakala F 2008 Phys. Rev. Lett. 100 197202
[39] Hartzstein C and Entin-Wohlman O 1985 Phys. Rev. B 32 491–494
[40] Galam S and Salinas S 1985 J. Phys. C: Solid State Phys. 18 L439–L442
[41] Swift M R, Maritan A, Cieplak M and Banavar J R 1994 J. Phys. A: Math. Gen. 27 1525–1532 [42] Bleher P M, Ruiz J and Zagrebnov V A 1998 J. Stat. Phys. 93 33–78
[43] Nowotny T, Patzlaff H and Behn U 2001 Phys. Rev. E 65 016127
[44] Rosinberg M L, Tarjus G and Perez-Reche F J 2009 J. Stat. Mech. P03003
[45] Kwon C and Thouless D J 1988 Phys. Rev. B 37 7649–7654
[46] Castellani T, Krzakala F and Ricci-Tersenghi F 2005 Eur. Phys. J. B 47 99–108
[47] Gillin P, Nishimori H and Sherrington D 2001 Journal of Physics A: Mathematical and General
34 2949
[48] Montanari A and Ricci-Tersenghi F 2004 Phys. Rev. B 70 134406
[49] Krzakala F and Zdeborov ́a L 2010 J. Chem. Phys. 134 034513
[50] Nishimori H 1981 Prog. Theor. Phys. 66 1169–1181
[51] Carlson J M, Chayes J T, Chayes L, Sethna J and Thouless D J 1990 J. Stat. Phys. 61 987–1067 [52] Carlson J M, Chayes J T, Sethna J P and Thouless D J 1990 J. Stat. Phys. 61 1069–1084
[53] Kabashima Y 2003 J. Phys. Soc. Jpn. 72 1645–1649
[54] Yang C N and Lee T D 1952 Phys. Rev. 87 404–409
[55] Lee T D and Yang C N 1952 Phys. Rev. 87 410–419
[56] Nishimori H and Ortiz G 2011 Elements of Phase Transitions and Critical Phenomena (Oxford
University Press)
[57] Krzakala F and Zdeborov ́a L 2008 Europhys. Lett. 81 57005
[58] Haanp ̈aa ̈ H, J ̈arvisalo M, Kaski P and Niemela ̈ I SAT Benchmarks based on 3-Regular Graphs, SAT Competition 2005 benchmark description.
[59] Zdeborov ́a L and Boettcher S 2010 J. Stat. Mech. 2010 P02020 [60] Mattis D C 1976 Physics Letters A 56 421–422
[61] Kirkpatrick S, Gelatt Jr C and Vecchi M 1983 Science 220 671

31

Ensemble Inequivalence in the Ferromagnetic p-spin Model in Random Fields
Zsolt Bertalan, Takehiro Kuma, Yoshiki Matsuda, Hidetoshi Nishimori
(Submitted on 20 Jan 2011 (v1), last revised 21 Jan 2011 (this version, v2))
https://arxiv.org/abs/1101.3809
J. Stat. Mech. (2011) P01016

[1] P. Hertel and W. Thirring 1971 Ann. Phys. 63 520.
[2] J. Barr ́e, D. Mukamel and S. Ruffo 2001 PRL 87 030601.
F. Leyvraz and S. Ruffo 2002 J. Phys. A 35 285.
[3] J. Barr ́e, F. Bouchet, T. Dauxois, and S. Ruffo 2005 J. Stat. Phys. 119 677.
[4] D. Mukamel, S. Ruffo and N. Schreiber 2005 Phys. Rev. Lett. 95 240604.
[5] A. Campa, T. Dauxois and S. Ruffo 2009 Phys. Rep. 480 57.
[6] D. Mukamel 2008 Statistical mechanics of systems with long-range interactions
Dynamics and Thermodynamics of Systems with Long-Range Interactions: Theory and Experiment (AIP Conference Series vol 970) ed A. Campa, A. Giansati, G. Morgi and F. S. Labini.
D.Mukamel 2009 Notes on the Statistical Mechanics of Systems with Long-Range Interactions Preprint arXiv:0905.1457v1.
[7] V. A. Antonov 1962 Vest. Leningr. Gos. Univ. 7 135; translated in: 1985 IAU Symposia 113 525.
[8] D. Lynden-Bell and R. Wood 1968 Mot. Not. Roy. Astr. Soc. 138 495.
[9] I. Ispolatov and E. G. D. Cohen 2001 Physica A 295 475.
[10] A. Lederhendler and D. Mukamel 2010 Phys. Rev. Lett. 105 150602.
A. Lederhendler, O. Cohen and D. Mukamel 2010 Phase Diagram of the ABC model with Nonconserving Processes Preprint arXiv:1009.5207v1.
[11] D. Lynden-Bell 1999 Physica A 264 293. W. Thirring 1970 Z. Phys. 235 339.
18
[12] T. Dauxois, S. Ruffo, E. Arimondo and M. Wilkens (eds) 2002 Lecture Notes in Physics vol 602 Dynamics and Thermodynamics of Systems with Long-Range In- teractions (New York: Springer).
T. Dauxois, S. Ruffo and L. Cugliandolo (eds) 2009 Les Houches Summer School Les Houches Summer School 2008) vol 90 Long-Range Interacting Systems (Oxford: Oxford University Press).
[13] R. S. Ellis, H. Touchette and B. Turkington 2004 Physica A 335 518. H. Touchette, R. S. Ellis and B. Turkington 2004 Physica A 340 138.
[14] F. Bouchet and J. Barr ́e 2005 J. Stat. Phys. 118 1073.
[15] M. Blume 1966 Phys. Rev. 141 517.
H. W. Capel 1966 Physica (Utr.) 32 966.
[16] M. Blume, V. J. Emery and R. B. Griffiths 1971 Phys. Rev. A 4 1071.
[17] P. de Buyl, D. Mukamel and S. Ruffo 2005 AIP Conference Proceedings 800 533.
F. Bouchet, T. Dauxois, D. Mukamel and S. Ruffo 2008 Phys. Rev. E 77 011125.
[18] H. Nishimori 2001 Statistical Physics of Spin Glasses and Information Processing:
An Introduction (New York: Oxford University Press).
[19] B. Derrida 1981 Phys. Rev. B 24 2614.
[20] D. J. Gross and M. M ́ezard 1984 Nucl. Phys. B 240 431.
[21] A. Aharony 1978 Phys. Rev. B 18 3318.
[22] L. E. Reichl 1998 A Modern Course in Statistical Physics (New York: Wiley).
[23] P. H. Chavanis 2002 Phys. Rev. E 65 056123.
[24] A. Hu ̈ller 1994 Z. Phys. B 90 401.
D. H. E. Gross and E. V. Votyakov 2001 Eur. Phys. J. B 15 115.

32

Microcanonical Analysis of Spin Glasses Using Gauge Symmetry
Hidetoshi Nishimori
(Submitted on 14 Jan 2011)
https://arxiv.org/abs/1101.2795
J. Phys. Soc. Jpn. 80 (2011) 023002

L. D. Landau and E. M. Lifshitz: Statistical Physics (Butterworth-Heinemann, Oxford, 1984)
W. Greiner: Thermodynamics and Statistical Mechanics (Springer, New York, 1995).
A. Campa, T. Dauxois and S. Ruffo: Phys. Rep. 480 (2009) 57.
V. A. Antonov: IAU Symposia 113 (1985) 525.
W. Thirring: Z. Phys. 235 (1970) 339.
D. Lynden-Bell and R. Wood: Mon. Not. Roy. Astr. Soc. 138 (1968) 495.
M. Schmidt, R. Kusche, T. Hippler, J. Donges, W. Kronmu ̈ller, B. Issendorff and H. Haberland:
Phys. Rev. Lett. 86 (2001) 1191.
Z. Bertalan, T. Kuma, Y. Matsuda and H. Nishimori: to be published in J. Stat. Mech.
J. Barr ́e, D. Mukamel and S. Ruffo: Phys. Rev. Lett. 87 (2001) 030601.
F. Leyvraz and S. Ruffo: J. Phys. A: Math. and Gen. 35 (2002) 285.
D. Mukamel, S. Ruffo and N. Schreiber: Phys. Rev. Lett. 95 (2005) 240604.
I. Ispolatov and E. G. D. Cohen: Physica A 295 (2001) 475.
H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169.
H. Nishimori: Statistical Physics of Spin Glasses and Information Processing: An Introduction
(Oxford University Press, Oxford, 2001).
S. F. Edwards and P. W. Anderson: J. Phys. F 5 (1975) 965.
D. Sherrington and S. Kirkpatrick: Phys. Rev. Lett. 35 (1975) 1792.

33

Real-space renormalization group for the transverse-field Ising model in two and three dimensions
Ryoji Miyazaki, Hidetoshi Nishimori, Gerardo Ortiz
(Submitted on 21 Dec 2010 (v1), last revised 31 Mar 2011 (this version, v2))
https://arxiv.org/abs/1012.4557
Phys. Rev. E 83, 051103 (2011)

[1] H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena (Oxford University Press, 2011).
[2] S. D. Drell, M. Weinstein, and S. Yankielowicz, Phys. Rev. D 16, 1769 (1977).
[3] R. Jullien, P. Pfeuty, J. N. Fields, and S. Doniach, Phys. Rev. B 18, 3568 (1978).
[4] G. Um, Phys. Rev. B 15, 2736 (1977).
[5] J. E. Hirsch and G. F. Mazenko, Phys. Rev. B 19, 2656 (1979).
[6] B. Hu, Phys. Lett. 71A, 83 (1979).
[7] E. Fradkin and S. Raby, Phys. Rev. D 20, 2566 (1979).
[8] A. Fernandez-Pacheco, Phys. Rev. D 19, 3173 (1979).
13
[9] S. R. White, Phys. Rev. Lett. 69, 2863 (1992); Phys. Rev. B 48, 10345 (1993).
[10] G. Vidal, Phys. Rev. Lett. 99, 220405 (2007); G. Evenbly and G. Vidal, Phys. Rev. B 79,
144108 (2009).
[11] K. A. Penson, R. Jullien, and P. Pfeuty, Phys. Rev. B 19, 4653 (1979).
[12] J. E. Hirsch, Phys. Rev. B 20, 3907 (1979).
[13] D. C. Mattis and J. Gallardo, J. Phys. C 13, 2519 (1980).
[14] H. W. J. Bl ̈ote, E. Luijten, and J. R. Heringa, J. Phys. A 28, 6289 (1995).
[15] A. Pelissetto and E. Vicari, Phys. Rep. 368 549 (2002).

34

Accelerated Stochastic Sampling of Discrete Statistical Systems
Zsolt Bertalan, Hidetoshi Nishimori, Henri Orland
(Submitted on 5 Oct 2010 (v1), last revised 20 Oct 2010 (this version, v2))
https://arxiv.org/abs/1010.0736
Physical Review E 82, (2010) 056704

[1] A. K. Hartmann and H. Rieger, Optimization Algorithms in Physics, (Wiley, Berlin, 2002).
[2] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem.
Phys. 21, 1087 (1953).
[3] A. F. Voter, in Radiation Effects in Solids, K.E. Sickafus and E.A. Kotomin (eds.), (Springer,
Dordrecht, 2005).
[4] S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Science 222, 220 (1983). V. Cerny, J. Opt.
Theor. App. 45, 41 (1985).
[5] K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, (1996).
[6] K. Hukushima and Y. Iba, in The Monte Carlo Method in the Physical Sciences, J.E. Guber-
natis (ed.), (The American Institute of Physics, 2003).
[7] A. R. Fersht and V. Daggett, Cell 108, 573 (2002).
[8] H. Orland, J. Phys. Soc. Jpn. 78, 103002 (2009).
[9] G. Reinelt, ORSA J. Comp. 3, 376 (1991). http://comopt.ifi.uni-heidelberg.de/
software/TSPLIB95
17
[10] S. Shinomoto and Y. Kabashima, J. Phys. A: Math. Gen. 24, L141 (1991).
[11] S. Geman and D. Geman, IEEE Trans. Patt. Anal. Mach. Intel. 6, 723 (1984).
[12] D. S. Johnson and L. A. McGeoch, in Local Search in Combinatorical Optimization, E.H.L.
Aarts and J.K. Lenstra (eds.), (John Wiley and Sons Inc., London, 1997).
[13] S. Lin and B. W. Kernighan, Oper. Res. 21, 498 (1973).
[14] R. H. Swendsen and J. S. Wang, Phys. Rev. Lett. 58, 86 (1987). U. Wolff, Phys. Rev. Lett.
62, 361 (1989).
[15] A. L. Talapov and H. W. J. Bl ̈ote, J. Phys A: Math. Gen. 29, 5727 (1996).
[16] G. Schwabl, Quantum Mechanics, (Springer, Heidelberg, 1995).

35

Quantum annealing: An introduction and new developments
Masayuki Ohzeki, Hidetoshi Nishimori
(Submitted on 9 Jun 2010)
https://arxiv.org/abs/1006.1696
Special Issue on Foundations of Computational and Theoretical Nanoscience on Journal of Computational and Theoretical Nanoscience

1 T. Kadowaki, and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
2 T. Kadowaki, Study of optimization problems by quan- tum annealing, PhD thesis, Tokyo Institute of Technology, (1999); e-print arXiv:0205020 [quant-ph].
3 A. B. Finnila, M. A. Gomez, C. Sebenik, S. Stenson, and J. D. Doll, Chem. Phys. Lett. 219, 343 (1994)
4 A. Das, and B. K. Charkrabarti, Quantum Annealing and Related Optimization Methods, Lecture Notes in Physics Vol.679 Springer, Berlin, (2005).
5 G. E. Santoro, and E. Tosatti, J. Phys. A 39, R393 (2006)
6 A. Das, and B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008)
7 S. Morita, and H. Nishimori, J. Math. Phys. 49, 125210 (2008)
8 A. K. Hartmann, and M. Weigt, Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics Wiley-VCH, Weinheim, (2005).
9 E. Farhi, J. Goldstone, S. Gutomann, and M. Sipser, e- print arXiv:0001106 [quant-ph].
10 M. R. Garey, and D. S. Johnson, Computers and In- tractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, (1979).
11 S. Kirkpatrick, S. D. Gelett, and M. P. Vecchi, Science,
220, 671 (1983)
12 E. Aarts, and J. Korst, Simulated Annealing and Boltz-
mann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing (Wiley, New York, 1984).
13 C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)
14 C. Jarzynski, Phys. Rev. E 56, 5018 (1997)
15 R. M. Neal, Statistics and Computing, 11, 125 (2001)
16 Y. Iba, Trans. Jpn. Soc. Artif. Intel.16, 279 (2001)
17 K. Hukushima, and Y. Iba, AIP. Conf. Proc. 690, 200
(2003)
18 M. Ohzeki, and H. Nishimori, e-print arXiv:1003.5453
[cond-mat.dis-nn].
19 M. Ohzeki, and H. Nishimori, work in progress.
20 J. Roland, and N. J. Cerf, Phys. Rev. A 65, 042308 (2002)
21 S. Suzuki, and M. Okada, J. Phys. Soc. Jpn. 74,1649 (2005)
22 L. K. Grover, Phys. Rev. Lett. 79, 325 (1997)
23 S. Morita, and H. Nishimori, J. Phys. A: Math. and Gen.
39, 13903 (2006)
24 S. Geman and D. Geman, IEEE Trans. Pattern Anal.
Mach. Intell. PAMI-6, 721 (1984)
25 S. Morita, and H. Nishimori, J. Phys. Soc. Jpn. 76 064002
(2007)
26 T. W. B. Kibble, Phys. Rep. 67, 183 (1980)
27 W. H. Zurek, Nature 317, 505 (1985)
28 W. H. Zurek, U. Dorner, and P. Zoller, Phys. Rev. Lett.
95, 105701 (2005)
29 J. Dziarmaga, Phys. Rev. Lett. 95, 245701 (2005)
30 J. Dziarmaga, Phys. Rev. B 74, 064416 (2006)
31 S. Suzuki, J. Stat. Mech. P03032 (2009)
32 G. Biroli, L. F. Cugliandolo, A. Sicilia, e-print
arXiv:1001.0693v1 [cond-mat.stat-mech].
33 B. Derrida, Phys. Rev. Lett. 45, 79 (1980)
34 T. J ̈org, F. Krzakala, J. Kurchan, and A. C. Maggs, Phys.
Rev. Lett. 101, 147204 (2008)
35 A. P. Young, S. Knysh, and V. N. Smelyanskiy, Phys. Rev.
Lett. 101, 170503 (2008)
36 A. P. Young, S. Knysh, and V. N. Smelyanskiy, Phys. Rev.
Lett. 104, 020502 (2010)
37 T. J ̈org, F. Krzakala, J. Kurchan, A. C. Maggs, and J.
Pujos, Euro. Phys. Lett. 89, 40004 (2010)
38 R. D. Somma, C. D. Batista, and G. Ortiz, Phys. Rev.
Lett. 99, 030603 (2007)
39 H. Orland, J. Phys. Soc. Jpn. 78, 103002 (2009)
40 R. C. Lua, and A. Y. Grosberg, J. Phys. Chem. B 109,
6805 (2005)
41 C. Jarzynski, Phys. Rev. E 73, 046105 (2006)
42 C. Chatelain, and D. Karevski, J. Stat. Mech. (2006)
P06005.
43 P. Wocjan, C. Chiang, D. Nagaj, and A. Abeyesinghe,
Phys. Rev. A 80, 022340 (2009) 44 M. Ohzeki, work in progress.

36

Zero-Temperature Complex Replica Zeros of the ±J Ising Spin Glass on Mean-Field Systems and Beyond
Tomoyuki Obuchi, Yoshiyuki Kabashima, Hidetoshi Nishimori, Masayuki Ohzeki
(Submitted on 19 Apr 2010)
https://arxiv.org/abs/1004.3118

[1] M. Me ́zard, G. Parisi and M. A. Virasoro, Spin Glass Theory and Beyond (Singapore: World Scientific, 1987)
[2] H. Nishimori, Statistical Physics of Spin Glasses and Information Pro- cessing: An Introduction (Oxford: Oxford University Press, 2001)
[3] J.-L. Barrat, M. Feigelman, J. Kurchan and J. Dalibard, Slow relax- ations and nonequilibrium dynamics in condensed matter (Springer- Verlag Berlin Heidelberg, New York, 2003) p. 271-365.
[4] M Me ́zard and A Montanari, Information, Physics, and Computation (Oxford: Oxford University Press, 2009).
[5] J. -P. Bouchaud and M Me ́zard, J. Phys. A 30 (1997) 7997.
[6] G. Parisi and T. Rizzo, Phys. Rev. Lett. 101 (2008) 117205.
[7] T. Nakajima and K. Hukushima, J. Phys. Soc. Jpn. 77 (2008) 074718.
[8] G. Parisi, J. Phys A 73 (1980) L115.
[9] G. Parisi, J. Phys. A 13 (1980) 1101.
[10] D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett 35 (1975) 1792.
[11] M. Talagrand, Ann. Math. 163 (2006) 221.
[12] K. Ogure and Y. Kabashima, Prog. Theor. Phys. 111 (2004) 661.
[13] K. Ogure and Y. Kabashima, J. Stat. Mech. (2009) P03017.
[14] C. N. Yang and T. D. Lee, Phys. Rev. 87 (1952) 404; ibid. 87 (1952) 410.
[15] K. Ogure and Y. Kabashima, J. Stat. Mech. (2009) P05011.
[16] T. Obuchi, Y. Kabashima, and H. Nishimori, J. Phys. A 42 (2009) 075004.
[17] A.N. Berker and S. Ostlund, J. Phys. C 12, (1979) 4961.
[18] R.B. Griffiths and M. Kaufman, Phys. Rev. B 26, (1982) 5022R.
[19] M. Kaufman and R.B. Griffiths, Phys. Rev. B 30, (1984) 244.
[20] E. Gardner, J. Physique 45 (1984) 1755.
[21] M. A. Moore, H. Bokil and B. Drossel, Phys. Rev. Lett. 81 (1998) 4252.
[22] D. R. Bowman and K. Levin K, Phys. Rev. B 25 (1982) 3438.
[23] A. Montanari and F. Ricci-Tersenghi, Euro. Phys. J. B 33 (2003) 339.
[24] S. R. Mckay, A. N. Berker and S. Kirkpatrick, Phys. Rev. Lett. 48, (1982) 767.
[25] F. D. Nobre, Phys. Rev. E 64, (2001) 046108.
[26] M. Ohzeki and H. Nishimori, J. Phys. A 42 (2009) 332001.
[27] Y. Matsuda, M. Mueller, H. Nishimori, T. Obuchi and A. Scardicchio,
arXiv:1001.4873

37

arXiv:1004.2389 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
10.1143/JPSJ.79.084003
Non-equilibrium Relations for Spin Glasses with Gauge Symmetry
Authors: Masayuki Ohzeki, Hidetoshi Nishimori
Submitted 14 April, 2010; originally announced April 2010.
Comments: 8 pages, 2 figures, submitted to JPSJ
Journal ref: J. Phys. Soc. Jpn., Vol.79, No.8, p.084003 2010
https://arxiv.org/abs/1004.2389

K. Binder, and A. P. Young: Rev. Mod. Phys. 58 (1986) 801.
A. P. Young (ed.): Spin Glasses and Random Fields (World Scientific, Singapore, 1997).
N. Kawashima, and H. Rieger: in Frustrated Spin Systems, ed. T. H. Diep (World Scientific, Singapore, 2004).
M. M ́ezard, G. Parisi and M. A. Virasoro: Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
R. H. Swendsen, and J. S. Wang: Phys. Rev. Lett. 58 (1987) 56.
K. Hukushima, and K. Nemoto: J. Phys. Soc. Jpn. 65 (1996) 1604.
R. M. Neal: Statistics and Computing, 11 (2001) 125.
Y. Iba: Trans. Jpn. Soc. Artif. Intel. 16 (2001) 279.
K. Hukushima, and Y. Iba: AIP. Conf. Proc. 690 (2003) 200.
Y. Ozeki and N. Ito: J. Phys. A: Math. Theor. 40 (2007) R149.
C. Jarzynski: Phys. Rev. Lett. 78 (1997) 2690.
C. Jarzynski: Phys. Rev. E 56 (1997) 5018.
G. E. Crooks: J. Stat. Phys. 90 (1998) 1481.
G. E. Crooks: Phys. Rev. E 60 (1999) 2721.
G. E. Crooks: Phys. Rev. E 61 (2000) 2361.
H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169.
H. Nishimori: Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford Univ. Press, Oxford, 2001).
Y. Ozeki: J. Phys. A: Math. Gen. 28 (1995) 3645.

38

arXiv:1003.5453 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
10.1016/j.physe.2010.07.051
Nonequilibrium relations in spin glasses
Authors: Masayuki Ohzeki, Hidetoshi Nishimori
Submitted 21 May, 2010; v1 submitted 29 March, 2010; originally announced March 2010.
Comments: 4 pages, Proceeding of International Symposium on Nanoscience and Quantum Physics (nanoPHYS'09) Version 3 is the final one
https://arxiv.org/abs/1003.5453

[1] A. K. Hartmann and M. Weigt, Phase Transitions in Combinatorial Opti- mization Problems: Basics, Algorithms and Statistical Mechanics Wiley- VCH, Weinheim, (2005).
[2] S. Kirkpatrick, C. D. Gelett, and M. P. Vecchi, Science 220 (1983) 671.
[3] C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).
[4] C. Jarzynski, Phys. Rev. E 56, 5018 (1997).
[5] R. M. Neal, Statistics and Computing, 11 125 (2001).
[6] Y. Iba, Trans. Jpn. Soc. Artif. Intel.16 279 (2001).
[7] K. Hukushima, and Y. Iba, AIP. Conf. Proc. 690, 200 (2003).
[8] H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981).
[9] H. Nishimori, Statistical Physics of Spin Glasses and Information Pro-
cessing: An Introduction (Oxford Univ. Press, Oxford, 2001).
[10] G. E. Crooks, J. Stat. Phys. 90, 1481 (1998); Phys. Rev. E 60, 2721
(1999).
[11] G. E. Crooks, Phys. Rev. E 61, 2361 (2000).
[12] K. Malick, M. Moshe, and H. Orland, e-print arXiv:0711.2059v2
[13] N. Metropolis, A. W. Rosenbluth, and M. N. Rosenbluth, A. H. Teller,
and E. Teller, J. Chem. Phys. 21, 1087 (1953).
[14] R. J. Glauber, J. Math. Phys. 4, 294 (1963).
[15] Y. Ozeki, J. Phys. A: Math. Gen. 28 3645 (1995).
[16] Y. Ozeki, J. Phys.: Condens. Matter 9 11171 (1997).
[17] Y. Ozeki, J. Phys. A; Math. Gen. 36 2673 (2003).
[18] M. Ohzeki, and H. Nishimori, e-print arXiv:1004.2389.

39

arXiv:1001.4873 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi
10.1088/1751-8113/43/28/285002
Distribution of partition function zeros of the ±J model on the Bethe lattice
Authors: Yoshiki Matsuda, Markus Mueller, Hidetoshi Nishimori, Tomoyuki Obuchi, Antonello Scardicchio
Submitted 15 June, 2010; v1 submitted 27 January, 2010; originally announced January 2010.
Comments: 23 pages, 12 figures
Journal ref: J. Phys. A: Math. Theor. 43 (2010) 285002
https://arxiv.org/abs/1001.4873

[1] LeeTDandYangCN1952Phys.Rev.87410
[2] Fisher M E 1964 The Nature of Critical Points (Lectures in Theoretical Physics vol 7C) (the University of Colorado Press, Boulder)
[3] Griffiths R B 1969 Phys. Rev. Lett. 23 17
[4] Bray A J and Huifang D 1989 Phys. Rev. B 40 6980
[5] Laumann C, Scardicchio A and Sondhi S L 2008 Phys. Rev. E 77 61139
[6] Chan P Y, Goldenfeld N and Salamon M 2006 Phys. Rev. Lett. 97 137201
[7] Ozeki Y and Nishimori H 1988 J. Phys. Soc. Jpn. 57 1087
[8] Matsuda Y, Nishimori H and Hukushima K 2008 J. Phys. A: Math. Theor. 41 324012 [9] Bhanot G and Lacki J 1993 J. Stat. Phys. 71 259
[10] Saul L and Kardar M 1993 Phys. Rev. E 48 R3221
[11] Damgaard P H and Lacki J 1995 Int. J. Mod. Phys. 6 819
[12] M ́ezard M and Parisi G 2001 Eur. Phys. J. B 20 217
[13] Chayes J T, Chayes L, Sethna J and Thouless D J 1986 Commun. Math. Phys. 106 41
[14] Obuchi T, Kabashima Y and Nishimori H 2009 J. Phys. A: Math. Theor. 42 5004
[15] Thouless D J 1986 Phys. Rev. Lett. 56 1082
[16] Carlson J M, Chayes J T, Chayes L, Sethna J and Thouless D J 1990 J. Stat. Phys. 61 987
[17] Carlson J M, Chayes J T, Sethna J P and Thouless D J 1990 J. Stat. Phys. 61 1069
[18] Kabashima Y 2003 J. Phys. Soc. Jpn. 72 1645
[19] Nishimori H 1981 Prog. Theor. Phys. 66 1169
[20] de Almeida J R L and Thouless D J 1978 J. Phys. A: Math. Gen. 11 983
[21] Sherrington D and Kirkpatrick S 1975 Phys. Rev. Lett. 35 1792
[22] Pagnani A, Parisi G and Rati ́eville M 2003 Phys. Rev. E 68 046706
[23] J ̈org T, Katzgraber H G and Krza ̧kal􏰀a F 2008 Phys. Rev. Lett. 100 197202
[24] M ́ezard M, Parisi G and Virasoro M A 1987 Spin Glass Theory and Beyond (Singapore: World
Scientific)
[25] Fisher K H and Hertz J A 1991 Spin Glasses (Cambridge: Cambridge University Press)
[26] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction
(Oxford University Press)
[27] Castellani T, Krzakala F and Ricci-Tersenghi F 2005 Eur. Phys. J. B 47 99 [28] Krza ̧kal􏰀a F 2005 Prog. Theor. Phys. Supp. No. 157 77
[29] Martin O C, M ́ezard M and Rivoire O 2005 J. Stat. Mech. 2005 P09006 [30] Rivoire O, Biroli G, Martin O C and Mezard M 2003 Eur. Phys. J. B 37 55 [31] Zdeborov ́a L 2009 Acta Physica Slovaca 59 169
[32] Kwon C and Thouless D J 1988 Phys. Rev. B 37 7649

40

arXiv:1001.0836 [pdf, ps, other] quant-ph
Quantum Annealing with Jarzynski Equality (CCP2009)
Authors: Masayuki Ohzeki, Hidetoshi Nishimori
Submitted 4 July, 2010; v1 submitted 6 January, 2010; originally announced January 2010.
Comments: 3 pages, 1 figure, Proceeding of Conference on Computational Physics 2009, Taiwan
https://arxiv.org/abs/1001.0836

[1] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness Freeman, (San Fran- cisco, 1979).
[2] A. B. Finnila, M. A. Gomez, C. Sebenik, S. Stenson, and J. D. Doll, Chem. Phys. Lett. 219, 343 (1994).
[3] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[4] S. Morita, and H. Nishimori, J. Math. Phys. 49, 125210 (2008).
[5] S. Suzuki and M. Okada, J. Phys. Soc. Jpn. 74, 1649 (2005).
[6] T. Jorg, F. Krzakala, J. Kurchan, A. C. Maggs, Phys. Rev. Lett.
101, 147204 (2008).
[7] A. P. Young, S. Knysh, and V. N, Smelyanskiy, Phys. Rev. Lett.
104, 020502 (2010).
[8] C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).
[9] C. Jarzynski, Phys. Rev. E 56, 5018 (1997).
[10] R. D. Somma, C. D. Batista, and G. Ortiz, Phys. Rev. Lett. 99, 030603 (2007).
[11] P. Wocjan, C. Chiang, D. Nagaj, and A. Abeyesinghe, Phys. Rev. A. 80, 022340 (2009).
[12] M. Ohzeki, work in progress.
[13] M. Ohzeki and S. Tanaka, work in progress.

41

arXiv:0911.5561 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi
10.1016/j.physa.2010.01.025
Multicritical point of spin glasses
Authors: Hidetoshi Nishimori, Masayuki Ohzeki
Submitted 30 November, 2009; v1 submitted 30 November, 2009; originally announced November 2009.
Comments: 6 pages, 3 figures, Dedicated to Prof. A. Nihat Berker on the occasion of his sixtieth birthday. to appear in Physica A
https://arxiv.org/abs/0911.5561

H. Nishimori and K. Nemoto, J. Phys. Soc. Jpn. 71, 1198 (2002).
J.-M. Maillard, K. Nemoto and H. Nishimori, J. Phys. A 36, 9799 (2003).
K. Takeda, T. Sasamoto and H. Nishimori, J. Phys. A 38, 3751 (2005).
H. Nishimori, J. Stat. Phys. 126, 977 (2007).
M. Ohzeki, H. Nishimori, and A. N. Berker, Phys. Rev. E 77, 061116 (2008).
M. Ohzeki, Phys. Rev. E 79 021129 (2009).
H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981).
H. Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford Univ. Press, Oxford, 2001).
M. Hinczewski and A. N. Berker, Phys. Rev. B 72, 144402 (2005).
M. Hasenbusch, F. P. Toldin, A. Pelissetto, and E. Vicari, Phys. Rev. E 77, 051115 (2008).
F. Parisen Toldin, A. Pelissetto, and E. Vicari, J. Stat. Phys. 135 1039 (2009).
S. L. A. de Queiroz, Phys. Rev. B 79, 174408 (2009).
M. Ohzeki and H. Nishimori, J. Phys. A: Math. Theor. 42 332001 (2009).
E. Domany, J. Phys. C 12, L119 (1979).
M. Ohzeki, H. G. Katzgraber, H. Bombin, and M. A. Martin-Delgado, work in progress.

42

arXiv:0905.3623 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi
10.1088/1751-8113/42/33/332001
Analytical evidence for the absence of spin glass transition on self-dual lattices
Authors: Masayuki Ohzeki, Hidetoshi Nishimori
Submitted 22 May, 2009; originally announced May 2009.
Comments: 11 Pages, 4 figures, 1 table. submitted to J. Phys. A Math. Theor
Journal ref: J. Phys. A: Math. Theor. 42 (2009) 332001
https://arxiv.org/abs/0905.3623

[1] Edwards S F and Anderson P W 1975 J. Phys. F 5 965
[2] Sherrington D and Kirkpatrick S 1975 Phys. Rev. Lett. 35 1792
[3] Binder K and Young A P 1986 Rev. Mod. Phys. 58 801
[4] Young A P (ed) 1997 Spin Glasses and Random Fields (Singapore: World Scientific)
[5] Kawashima N and Rieger H 2004 in Frustrated Spin Systems Diep T H ed (Singapore: World
Scientific)
[6] McMillan W L 1983 Phys. Rev. B 29 4026
[7] Bray A J and Moore M A 1984 J. Phys. C: Solid State Phys. 17 L463 [8] McMillan W L 1984 Phys. Rev. B 30 476
[9] Bhatt R N and Young A P 1988 Phys. Rev. B 37 5606
[10] Hartmann A K and Young A P 2001 Phys. Rev. B 64 180404 [11] Houdayer J and Hartmann A K 2004 Phys. Rev. B 70 014418 [12] Singh R R P and Chakravarty S 1986 Phys. Rev. Lett. 57 245 [13] Kawashima N and Rieger H 1997 Europhys. Lett. 39 85
[14] Sungthong R and Poulter J 2003 J. Phys. A: Math. Gen. 36 6675
[15] Nishimori H 1981 Prog. Theor. Phys. 66 1169
[16] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction
(Oxford: Oxford University Press)
[17] Kramers H A and Wannier G H 1941 Phys. Rev. 60 252
[18] Wu F Y and Wang Y K 1976 J. Math. Phys. 17 439
[19] Wu F Y 1982 Rev. Mod. Phys. 54 235
[20] Berker A N and Ostlund S 1979 J. Phys. C 12 4961
[21] Griffiths R B and Kaufman M 1982 Phys. Rev. B 26 5022
[22] Kaufman M and Griffiths R B 1984 Phys. Rev. B 30 244
[23] Nishimori H and Nemoto K 2002 J. Phys. Soc. Jpn. 71 1198
[24] Maillard J-M, Nemoto K and Nishimori H 2003 J. Phys. A 36 9799
[25] Takeda K and Nishimori H 2004 Nucl. Phys. B 686 377
[26] Takeda K, Sasamoto T and Nishimori H 2005 J. Phys. A 38 3751
[27] Nishimori H and Ohzeki M 2006 J. Phys. Soc. Jpn. 75 034004
[28] Nishimori H 2007 J. Stat. Phys. 126 977
[29] Ohzeki M, Nishimori H and Berker A N 2008 Phys. Rev. E 77 061116
[30] Ohzeki M 2009 Phys. Rev. E 79 021129
[31] Hasenbusch M, Toldin F P, Pelissetto A and Vicari E 2008 Phys. Rev. E 77, 051115 [32] de Queiroz S L A 2009 Phys. Rev. B 79, 174408
[33] Georges A, Hansel D, Le Doussal P, and Maillard J-M 1987 J. Physique 48 1
[34] Wood D W and Griffiths H P 1972 J. Phys. C: Solid State Phys. 5 L253
[35] Merlini D and Gruber C 1972 J. Math. Phys. 13 1814
[36] Ohzeki M Preprint cond-mat/0903.2102v2
[37] Katzgraber H G, Bombin H and Martin-Delgado M A Preprint cond-mat/0902.4845v1 [38] Hasegawa T and Nemoto K 2006 J. Phys. Soc. Jpn. 75 074701

43

arXiv:0809.2635 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi
10.1088/1751-8113/42/7/075004
Complex Replica Zeros of ±J Ising Spin Glass at Zero Temperature
Authors: Tomoyuki Obuchi, Yoshiyuki Kabashima, Hidetoshi Nishimori
Submitted 14 November, 2008; v1 submitted 16 September, 2008; originally announced September 2008.
Comments: 27 pages, 13 figures. Added references, some comments, and corrections to minor errors
Journal ref: J. Phys. A: Math. Theor. 42 (2009) 075004
https://arxiv.org/abs/0809.2635

[1] M ́ezard M, Parisi G and Virasoro M A 1987 Spin Glass Theory and Beyond (Singapore: World Scientific)
[2] Sherrington D and Kirkpatrick S 1975 Phys. Rev. Lett. 35 1792 [3] Parisi G 1980 J. Phys. A: Math. Gen. 73 L115
[4] Parisi G 1980 J. Phys. A: Math. Gen. 13 1101
[5] Talagrand M 2006 Ann. Math. 163 221
[6] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford: Oxford University Press)
[7] Sourlas N 1989 Nature 339 693
[8] Kabashima Y and Saad D 1999 Europhys. Lett. 45 97
[9] Nishimori H and Wong K Y M 1999 Phys. Rev. E 60 132
[10] Titchmarsh E C 1939 The Theory of Functions 2nd. ed. (Oxford: Oxford University Press) [11] van Hemmen J L and Palmer R G 1979 J. Phys. A: Math. Gen. 12 563
[12] Ogure K and Kabashima Y 2004 Prog. Theor. Phys. 111 661
[13] Moukarzel C and Parga N 1991 Physica A 177 24
[14] Moukarzel C and Parga N 1991 Physica A 185 305
[15] Derrida B 1981 Phys. Rev. B 24 2613
[16] Ogure K and Kabashima Y 2005 Prog. Theor. Phys. Supplement 157 103
[17] Bowman D R and Levin K 1982 Phys. Rev. B 25 3438
[18] Chayes J T, Chayes L, Sethna J P and Thouless D J 1986 Commun. Math. Phys. 106 41
[19] Mottishaw P 1987 Europhys. Lett. 4 333
[20] Carlson J M, Chayes J T, Chayes L, Sethna J P and Thouless D J 1998 Europhys. Lett. 5 355 [21] Lai P and Goldschmidt Y Y 1989 J. Phys. A: Math. Gen. 22 399
[22] Parisi G and Rizzo T 2007 Large Deviations in the Free-Energy of Mean-Field Spin-Glasses
Preprint arXiv:0706.1180
[23] Fisher M E 1965 Lectures in Theoretical Physics vol. 7 (Boulder: University of Colorado Press) [24] Matveev V and Shrock R 1995 Phys. Rev. E 53 254
[25] Wong K Y M and Sherrington D 1987 J. Phys. A: Math. Gen. 20 L793
[26] M ́ezard M and Parisi G 2001 Euro. Phys. J. B 20 217
[27] M ́ezard M and Parisi G 2003 J. Stat. Phys. 111 1
[28] Montanari A and Ricci-Tersenghi F 2003 Euro. Phys. J. B 33 339
[29] Katsura S, Inawashiro S and Fujiki S 1979 Physica 99A 193
[30] Nakanishi K 1980 Phys. Rev. B 23 3514
[31] Yedidia J S, Freeman W T and Weiss Y 2005 IEEE Trans. Inform. Theory 51 2282
[32] M ́ezard M and Montanari A 2006 J. Stat. Phys. 124 1317
[33] Nakajima T and Hukushima K 2008 J. Phys. Soc. Japan 77 074718
[34] Monasson R 1995 Phys. Rev. Lett. 75 2847
[35] Thouless D J 1986 Phys. Rev. Lett. 56 1082
[36] Rivoire O, Biroli G, Martin O C and M ́ezard M 2004 Eur. Phys. J. B 37 55
[37] Krzakala F, Montanari A, Ricci-Tersenghi F, Semerjian G and Zdebrova L 2007 Proc. Natl. Acad.
Sci. 104 10318
[38] Martin O C, M ́ezard M and Rivoire O 2005 J. Stat. Mech P09006
[39] Gardner E 1985 Nucl. Phys. B 257 747
[40] Kadowaki T, Nonomura Y and Nishimori H 1996 J. Phys. Soc. Japan 65 1609

44

arXiv:0808.0365 [pdf, ps, other] quant-ph cond-mat.dis-nn
doi
10.1088/1742-6596/143/1/012003
Ground-state statistics from annealing algorithms: Quantum vs classical approaches
Authors: Yoshiki Matsuda, Hidetoshi Nishimori, Helmut G Katzgraber
Submitted 13 July, 2009; v1 submitted 3 August, 2008; originally announced August 2008.
Comments: 12 pages, 16 epsfiles
Journal ref: New J. Phys. 11 (2009) 073021
https://arxiv.org/abs/0808.0365

[1] Kadowaki T and Nishimori H 1998 Phys. Rev. E 58 5355
[2] Finnila A B, Gomez M A, Sebenik C, Stenson C and Doll J D 1994 Chem. Phys. Lett. 219 343 [3] Kirkpatrick S, Gelatt, Jr C D and Vecchi M P 1983 Science 220 671
[4] Das A and Chakrabarti B K 2005 Quantum Annealing and Related Optimization Methods (Edited
by A. Das and B.K. Chakrabarti, Lecture Notes in Physics 679, Berlin: Springer) [5] Santoro G, Martonˇa ́k R Tosatti E and Car R 2002 Science 295 2427
[6] Martonˇa ́k R, Santoro G E and Tosatti E 2002 Phys. Rev. B 66 094203
[7] Santoro G E and Tosatti E 2006 J. Phys. A 39 R393
[8] Das A and Chakrabarti B K 2008 Rev. Mod. Phys. 80 1061
[9] Young A P, Knysh S and Smelyanskiy V N 2008 Phys. Rev. Lett. 101 170503
[10] Morita S and Nishimori H 2008 J. Math. Phys. 49 125210
[11] Geman S and Geman D 1984 IEEE Trans. Pattern. Analy. Mach. Intell. PAMI-6 721
[12] Stella L, Santoro G E and Tosatti E 2005 Phys. Rev. B 72 014303
[13] Roland J and Cerf N J 2002 Phys. Rev. A 65 042308
[14] Villain J 1977 J. Phys. C 10 1717
[15] Kadowaki T 1998 Study of Optimization Problems by Quantum Annealing Ph.D. thesis Tokyo
Institute of Technology (quant-ph/0205020)
[16] Moreno J J, Katzgraber H G and Hartmann A K 2003 Int. J. Mod. Phys. C 14 285 [17] Moessner R and Sondhi S L 2001 Phys. Rev. Lett. 86 1881
[18] Moessner R and Sondhi S L 2003 Phys. Rev. B 68 184512

45

arXiv:0806.1859 [pdf, ps, other] quant-ph cond-mat.dis-nn
doi
10.1063/1.2995837
Mathematical Foundation of Quantum Annealing
Authors: Satoshi Morita, Hidetoshi Nishimori
Submitted 11 June, 2008; originally announced June 2008.
Comments: 51pages, 8 figures
https://arxiv.org/abs/0806.1859

[1] M. R. Garey and D. S. Johnson: Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979)
[2] A. K. Hartmann and M. Weigt: Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics (Wiley-VCH, Weinheim, 2005)
[3] K. Helsgaun: Euro. J. Op. Res. 126 (2000) 106.
[4] S. Kirkpatrick, S. D. Gelett and M. P. Vecchi: Science 220 (1983) 671
[5] E. Aarts and J. Korst: Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing (Wiley, New York, 1984)
[6] A. B. Finnila, M. A. Gomez, C. Sebenik, S. Stenson, and J. D. Doll: Chem. Phys. Lett. 219 (1994) 343
[7] T. Kadowaki and H. Nishimori: Phys. Rev. E 58 (1998) 5355
[8] T. Kadowaki: Study of Optimization Problems by Quantum Annealing (Thesis,
Tokyo Institute of Technology, 1999); quant-ph/0205020
[9] A. Das and B. K. Charkrabarti: Quantum Annealing and Related Optimization Meth-
ods (Springer, Berlin, Heidelberg, 2005) Lecture Notes in Physics, Vol. 679
[10] G. E. Santoro and E. Tosatti: J. Phys. A 39 (2006) R393
[11] A. Das and B. K. Chakrabarti: arXiv:0801.2193 (to be published in Rev. Mod. Phys.).
[12] B. Apolloni, C. Carvalho and D. de Falco: Stoch. Proc. Appl. 33 (1989) 233
[13] B. Apolloni, N. Cesa-Bianchi and D. de Falco: in Stochastic Processes, Physics and Geometry, eds. S. Albeverio et al. (World Scientific, Singapore, 1990) 97
[14] G. E. Santoro, R. Martonˇa ́k, E. Tosatti and R. Car: Science 295 (2002) 2427
[15] R. Martonˇa ́k, G. E. Santoro and E. Tosatti: Phys. Rev. B 66 (2002) 094203
[16] S. Suzuki and M. Okada: J. Phys. Soc. Jpn. 74 (2005) 1649
[17] M. Sarjala, V. Pet ̈aja ̈ and M. Alava: J. Stat. Mech. (2006) P01008
[18] S. Suzuki, H. Nishimori, and M. Suzuki: Phys. Rev. E 75 (2007) 051112
[19] R. Martonˇa ́k, G. E. Santoro and E. Tosatti: Phys. Rev. E 70 (2004) 057701
[20] L. Stella, G. E. Santoro and E. Tosatti: Phys. Rev. B 72 (2005) 014303
[21] L. Stella, G. E. Santoro and E. Tosatti: Phys. Rev. B 73 (2006) 144302
[22] A. Das, B. K. Chakrabarti and R. B. Stinchcombe: Phys. Rev. E 72 (2005) 026701
[23] H. F. Trotter: Proc. Am. Math. Soc. 10 (1959) 545
[24] M. Suzuki: Prog. Theor. Phys. 46 (1971) 1337
[25] D. P. Landau and K. Binder: A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge, Cambridge University Press, 2000) Chap. 8
[26] E. Farhi, J. Goldstone, S. Gutomann and M. Sipser: quant-ph/0001106
[27] A. Mizel, D. A. Lidar and M. Mitchel: Phys. Rev. Lett. 99 (2007) 070502.
[28] S. Morita: Analytic Study of Quantum Annealing (Thesis, Tokyo Institute of Tech- nology, 2008).
[29] S. Morita and H. Nishimori: J. Phys. Soc. Jpn. 76 (2007) 064002.
[30] A. Messiah: Quantum Mechanics (Wiley, New York, 1976)
[31] R. D. Somma, C. D. Batista, and G. Ortiz: Phys. Rev. Lett. 99 (2007) 030603
[32] E. Hopf: J. Math. Mech. 12 (1963) 683
[33] S. Geman and D. Geman: IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6 (1984) 721
[34] H. Nishimori and J. Inoue: J. Phys. A: Math. Gen. 31 (1998) 5661
[35] H. Nishimori and Y. Nonomura: J. Phys. Soc. Jpn. 65 (1996) 3780
[36] E. Seneta: Non-negative Matrices and Markov Chains (Springer, New York, 2006)
[37] S. Morita, J. Phys. Soc. Jpn. 76 (2007) 104001
[38] L. D. Landau and E. M. Lifshitz: Quantum Mechanics: Non-Relativistic Theory (Pergamon Press, Oxford, 1965)
[39] C. Zener: Proc. R. Soc. London Ser. A 137 (1932) 696
[40] S. Morita and H. Nishimori, J. Phys. A: Math. and Gen. 39 (2006) 13903
[41] H. W. Press, A. S. Tuekolosky, T. W. Vettering and P. B. Flannery: Numerical Recipes in C (Cambridge University Press, Cambridge, 1992) 2nd ed.
[42] L. K. Grover: Phys. Rev. Lett. 79 (1997) 325
[43] J. Roland and N. J. Cerf: Phys. Rev. A 65 (2002) 042308
[44] C. Tsallis and D. A. Stariolo: Physica A 233 (1996) 395
[45] D. M. Ceperley and B. J. Alder: Phys. Rev. Lett. 45 (1980) 566
[46] N. Trivedi and D. M. Ceperley: Phys. Rev. B 41 (1990) 4552
[47] L. Stella and G. E. Santoro: Phys. Rev. E 75 (2007) 036703

46

arXiv:0805.0754 [pdf, ps, other] cond-mat.dis-nn
Spin Glass Identities and the Nishimori Line
Authors: Pierluigi Contucci, Cristian Giardina, Hidetoshi Nishimori
Submitted 13 May, 2008; v1 submitted 6 May, 2008; originally announced May 2008.
Comments: 23 pages
https://arxiv.org/abs/0805.0754

[ABC] E.Agliari, A.Barra, F.Camboni. “Criticality in diluted ferromagnet”, http://arxiv.org/abs/0804.4503.
[AC] M.Aizenman, P.Contucci, “On the Stability of the Quenched state in Mean Field Spin Glass Models”, J. Stat. Phys., Vol. 92, N. 5/6, 765-783, (1998).
[Ba] A.Barra. ”Irreducible free energy expansion and overlap locking in mean field spin glasses”, J. Stat. Phys., Vol. 123, 601-614, (2006).
[B] A. Bovier, Statistical mechanics of disordered systems, MaPhySto Lecture Notes Vol. 10 (2001), Aarhus.
[C2] P.Contucci, “Replica Equivalence in the Edwards-Anderson Model”, J. Phys. A: Math. Gen., Vol. 36, 10961-10966, (2003).
[CGi]　P. Contucci, C. Giardina, “Spin-Glass Stochastic Stability: a Rigorous Proof” Annales Henri Poincare Vol. 6, No. 5, 915 - 923 (2005) [CGi2]　P. Contucci, C. Giardina, “The Ghirlanda-Guerra identities” Journ. Stat. Phys. 126, 917-931 (2007)
[EA]S.Edwards and P.W.Anderson “Theory of spin glasses”, J. Phys. F, Vol. 5, 965- 974, (1975)
[FMPP1] S.Franz, M.Mezard, G.Parisi, L.Peliti, “Measuring equilibrium properties in aging systems”, Phys. Rev. Lett., Vol. 81, 1758 (1998).
[FMPP2] S.Franz, M.Mezard, G.Parisi, L.Peliti, “The response of glassy systems to ran- dom perturbations: A bridge between equilibrium and off-equilibrium”, J. Stat. Phys. Vol. 97, N. 3/4, 459-488 (1999).
[G] F.Guerra, “About the overlap distribution in a mean field spin glass model”, Int. J. Phys. B, Vol. 10, 1675–1684 (1997).
[GG] S. Ghirlanda, F. Guerra, “General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity”, J. Phys. A: Math. Gen., Vol. 31, 9149-9155 (1998).
[GT2] F. Guerra, F.L. Toninelli, “The infinite volume limit in generalized mean field disordered models”, Markov Proc. Rel. Fields, Vol. 9, no. 2, 195-207 (2003).
[KS] K.M Khanin, Ya.G. Sinai, “Existence of free energy for models with long-range random Hamiltonians”, Journ. Stat. Phys., Vol. 20, 573-584, (1979)
[MPV] M.Mezard, G.Parisi, M.A.Virasoro, Spin Glass theory and beyond, World Scien- tific, Singapore (1987).
[MPRRZ] E. Marinari, G. Parisi, F. Ricci-Tersenghi, J. Ruiz-Lorenzo and F. Zuliani, Jour. Stat. Phys. 98 973 (2000)
[N1] H. Nishimori Statistical Physics of Spin Glasses and Information Processing, Oxford University Press, New York (2001)
[N2] H. Nishimori, “Internal Energy, Specific Heat and Correlation Function of the Bond-Random Ising Model”, Progress of Theoretical Physics, Vol. 66 No. 4 1169-1181 (1981)
[OTW] E. Orlandini, M.C. Tesi, S.G. Whittington, “Self averaging in the statistical mechanics of some lattice models”, J. Phys. A: Math. Gen. Vol. 35 1-9 (2002)
[Pa] G.Parisi, “On the probabilistic formulation of the replica approach to spin glasses”, Int. Jou. Mod. Phys. B, Vol. 18, 733-744, (2004).
[PS] L.A. Pastur, M.V. Scherbina, “Absence of self-averaging of the order parameter in the Sherrington-Kirkpatrick model”, Jour. Stat. Phys. Vol 62, Nos 1/2, 1-19, (1991)
[RU] D. Ruelle, Statistical Mechanics, Rigorous Results, W.A. Benjamin, New York 1969
[S] M. Scherbina, “On the replica symmetric solution for the Sherrington- Kirkpatrick model”, Helv. Phys. Acta Vol. 70, 838-853 (1997)
[SK] D.Sherrington and S.Kirkpatrick, “Solvable model of a spin-glass,” Phys. Rev. Lett., Vol. 35, 1792–1796 (1975).
[T] M.Talagrand, Spin glasses: a challenge for mathematicians, Springer, Berlin (2003).

47

arXiv:0802.2760 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi
10.1103/PhysRevE.77.061116
Multicritical points for the spin glass models on hierarchical lattices
Authors: Masayuki Ohzeki, Hidetoshi Nishimori, A. Nihat Berker
Submitted 4 March, 2009; v1 submitted 20 February, 2008; originally announced February 2008.
Comments: 11 pages, 9 figures, 7 tables This is the published version
Journal ref: Phys. Rev. E 77, 061116 (2008)
https://arxiv.org/abs/0802.2760

[1] S. F. Edwards and P. W. Anderson, J. Phys. F 5, 965 (1975).
[2] D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).
[3] A. P. Young (ed), Spin Glasses and Random Fields (World Scientific, Singapore, 1997).
[4] H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981).
[5] H. Nishimori, Statistical Physics of Spin Glasses and In- formation Processing: An Introduction (Oxford Univ.　Press, Oxford, 2001).
[6] P. Le Doussal and A. B. Harris, Phys. Rev. Lett. 61, 625
(1988).
[7] H. Nishimori and K. Nemoto, J. Phys. Soc. Jpn. 71, 1198
(2002).
[8] J.-M. Maillard, K. Nemoto and H. Nishimori, J. Phys. A
36, 9799 (2003).
[9] H. Nishimori, J. Stat. Phys. 126, 977 (2007).
[10] K. Takeda, T. Sasamoto and H. Nishimori, J. Phys. A 38, 3751 (2005).
[11] H. Nishimori and M. Ohzeki: J. Phys. Soc. Jpn. 75, 034004 (2006).
[12] M. Hinczewski and A. N. Berker, Phys. Rev. B 72, 144402 (2005).
Feza Gu ̈rsey Institute in Turkey, acknowledges Dr. M. Hinczewski of Feza Gu ̈rsey Institute for useful and fruit- ful discussions, Mr. S. Morita, and to Mr. Y. Matsuda of Tokyo Institute of Technology for many discussions and comments. This work was partially supported by CREST, JST, by the 21st Century COE Program at Tokyo Institute of Technology ‘Nanometer-Scale Quan- tum Physics’, and by the Grant-in-Aid for Scientific Re- search on the Priority Area “Deepening and Expansion of Statistical Mechanical Informatics” by the Ministry of Education, Culture, Sports, Science and Technology.
[13] F. D. Nobre, Phys. Rev. E 64, 046108 (2001).
[14] S. L. A. de Queiroz, Phys. Rev. B 73, 064410 (2006). [15] N. Ito and Y. Ozeki, Physica A321, 262 (2003).
[16] F. Merz and J. T. Chalker, Phys. Rev. B 65, 054425
(2002).
[17] A. Honecker, M. Picco and P. Pujol, Phys. Rev. Lett. 87,
047201 (2001).
[18] F. D. A. Aara ̃o Reis, S. L. A. de Queiroz and R.R. dos
Santos, Phys. Rev. B, 60 6740 (1999).
[19] M. Picco and A. Honecker and P. Pujol, J. Stat. Mech.
65, P09006 (2006).
[20] A.N. Berker and S. Ostlund, J. Phys. C 12, 4961 (1979). [21] R.B. Griffiths and M. Kaufman, Phys. Rev. B 26, 5022R
(1982).
[22] M. Kaufman and R.B. Griffiths, Phys. Rev. B 30, 244
(1984).
[23] M. Hinczewski and A.N. Berker, Phys. Rev. E 73, 066126
(2006).
[24] G. Migliorini and A.N. Berker, Phys. Rev. B 57, 426
(1998).
[25] E. Domany, J. Phys. C 12, L119 (1979).

48

arXiv:0802.0771 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi
10.1103/PhysRevE.77.061110
Reentrant and Forward Phase Diagrams of the Anisotropic Three-Dimensional Ising Spin Glass
Authors: Can Güven, A. Nihat Berker, Michael Hinczewski, Hidetoshi Nishimori
Comments: Added 7 more references. Published version. 7 pages, 7 figures, 1 table
Journal ref: Phys. Rev. E 77, 061110 (2008)
https://arxiv.org/abs/0802.0771

[1] H. Nishimori, Statistical Physics of Spin Glasses and In- formation Processing (Oxford University Press, 2001).
[2] H. Nishimori, J. Phys. C 13, 4071 (1980).
[3] H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981).
[4] H. Nishimori, J. Phys. Soc. Japan 55, 3305 (1986).
[5] Y. Ozeki and H. Nishimori, J. Phys. A 26, 3399 (1993).
[6] H. Nishimori, Physica A 205, 1 (1994).
[7] H. Nishimori and K. Nemoto, J. Phys. Soc. Japan 71,
1198 (2002).
[8] J.-M. Maillard, K. Nemoto, and H. Nishimori, J. Phys.
A: Math. Gen. 36, 9799 (2003).
[9] K. Takeda and H. Nishimori, Nucl. Phys. B 686, 377
(2004).
[10] K. Takeda, T. Sasamoto, and H. Nishimori, J. Phys. A:
Math. Gen. 38, 3751 (2005).
[11] M. Hinczewski and A.N. Berker, Phys. Rev. B 72, 144402
(2005).
[12] H. Nishimori, J. Stat. Phys. 126, 977 (2007).
[13] K. Binder and K. Schroder, Phys. Rev. B 14, 2142　(1976).
[14] I. Morgenstern and K. Binder, Phys. Rev. Lett. 43, 1615　(1979).
[15] C. Brangian, W. Kob, and K. Binder, J. Phys. A 36,　10847 (2003).
[16] H.G.Katzgraber,M.Ko ̈rner,andA.P.Young,Phys.　Rev. B 73, 224432 (2006).
[17] M. Hasenbusch, A. Pelissetto, and E. Vicari, J. Stat.
Mech. L02001 (2008).
[18] H.G. Katzgraber, A.K. Hartmann, and A.P. Young,　arXiv:0803.3417v1 [cond-mat.dis-nn] (2008).
[19] G. Migliorini and A.N. Berker, Phys. Rev. B 57, 426　(1998).
[20] F.D. Nobre, Phys. Rev. E 64, 046108 (2001).
[21] M. Ohzeki, J. Phys. Soc. Japan 76, 114003 (2007).
[22] M. Hinczewski and A.N. Berker, Eur. Phys. J. B 51, 461　(2006).
[23] M. Hinczewski and A.N. Berker,　arXiv:cond-mat/0607171v1 [cond-mat.str-el].
[24] A.N. Berker and S. Ostlund, J. Phys. C 12, 4961 (1979).
[25] R.B. Griffiths and M. Kaufman, Phys. Rev. B 26, 5022R (1982).
[26] M. Kaufman and R.B. Griffiths, Phys. Rev. B 30, 244 (1984).
[27] S.R. McKay, A.N. Berker, and S. Kirkpatrick, Phys. Rev. Lett. 48, 767 (1982).
[28] C. Monthus and T. Garel, arXiv:0711.2878v2 [cond- mat.dis-nn].
[29] A. Falicov, A.N. Berker, and S.R. McKay, Phys. Rev. B 51, 8266 (1995).
[30] E. Domany, S. Alexander, D. Bensimon, and L.P. Kadanoff, Phys. Rev. B 28, 3110 (1983).
[31] J.-M. Langlois, A.-M.S. Tremblay, and B.W. Southern, Phys. Rev. B 28, 218 (1983).
[32] R.B. Stinchcombe and A.C. Maggs, J. Phys. A 19, 1949 (1986).
[33] R.F. Angulo and E. Medina, J. Stat. Phys. 75, 135 (1994).
[34] T.A.S. Haddad, S.T.R. Pinho, and S.R. Salinas, Phys. Rev. E 61, 3330 (2000).
[35] J.-X. Le and Z.R. Yang, Phys. Rev. E 69, 066107 (2004). [36] B. Derrida and R.B. Griffiths, Europhys. Lett. 8, 111 (1989).
[37] R.A. da Silveira and J.-P. Bouchaud, Phys. Rev. Lett. 93, 015901 (2004).
[38] L.-H. Tang and H. Chat ́e, arXiv:cond-mat/0007350v1 [cond-mat.stat-mech].
[39] C. Monthus and T. Garel, J. Stat. Mech.: Theory and Experiment, P01008 (2008).
[40] M. Hinczewski and A.N. Berker, Phys. Rev. E 73, 066126 (2006).
[41] M. Hinczewski, Phys. Rev E 75, 061104 (2007).
[42] Z.Z. Zhang, L.L. Rong, and S.G. Zhou, Physica A 377, 329 (2007).
[43] Z.Z. Zhang, S.G. Zhou, and T. Zou, Eur. Phys. J. B 56, 259 (2007).
[44] Z.Z. Zhang, Z.G. Zhou, and L.C. Chen, Eur. Phys. J. B58, 337 (2007).
[45] H.D. Rozenfeld, S. Havlin, and D. ben-Avraham, New J. Phys. 9, 175 (2007).
[46] H.D. Rozenfeld and D. ben-Avraham, Phys. Rev. E 75, 061102 (2007).
[47] E. Khajeh, S.N. Dorogovtsev, and J.F.F. Mendes, Phys. Rev. E 75, 041112 (2007).
[48] A. Erba ̧s, A. Tuncer, B. Yu ̈cesoy, and A.N. Berker, Phys. Rev. E 72, 026129 (2005).

49

arXiv:0712.4063 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi 10.1088/1751-8113/41/32/324012
Distribution of Lee-Yang zeros and Griffiths singularities in the ±J model of spin glasses
Authors: Yoshiki Matsuda, Hidetoshi Nishimori, Koji Hukushima
Submitted 14 February, 2008; v1 submitted 25 December, 2007; originally announced December 2007.
Comments: 18 pages, 37 epsfiles Journal ref: J. Phys. A: Math. Theor. 41 (2008) 324012
https://arxiv.org/abs/0712.4063

[1] LeeTDandYangCN1952Phys.Rev.87410
[2] Ozeki Y and Nishimori H 1988 J. Phys. Soc. Japan 57 1087
[3] Griffiths R B 1969 Phys. Rev. Lett. 23 17
[4] Bray A J and Huifang D 1989 Phys. Rev. B 40 6980
[5] Bray A J and Moore M A 1982 J. Phys. C: Solid State Phys. 15 L765 [6] Hukushima K and Iba Y 2008 J. Phys.: Conference Series 95 012005 [7] Randeria M, Sethna J P and Palmer R G 1985 Phys. Rev. Lett. 54 1321 [8] Bhanot G and Lacki J 1993 J. Stat. Phys. 71 259
[9] Damgaard P H and Lacki J 1995 Int. J. Modern Phys. C 6 819
[10] Fisher M E 1964 The Nature of Critical Points (Lectures in Theoretical Physics vol 7C) ed Brittin W E and Dunham L G (the University of Colorado Press, Boulder, 1965)
[11] Hartmann A K 2002 Phys. Rev. E 65 056102
[12] K ̈orner M, Katzgraber H G and Hartmann A K 2006 J. Stat. Mech. P04005
[13] Monthus C and Garel T 2006 Phys. Rev. E 74 051109
[14] Iba Y and Hukushima K 2007 Preprint arXiv:0709.2578
[15] Binder K 1972 Physica 62 508
[16] Morgenstern I and Binder K 1979 Phys. Rev. Lett. 43 1615
[17] Creswick R J 1995 Phys. Rev. E 52 R5735
[18] Kawashima N and Rieger H 2004 Frustrated Spin Systems ed Diep H T (Singapore: World Scientific) Chapter 9
[19] Creswick R J and Kim S -Y 1997 Phys. Rev. E 56 2418
[20] de Almeida J R L and Thouless D J 1978 J. Phys. A: Math. Gen. 11 983
[21] Janke W, Johnston D A and Kenna R 2004 Nucl. Phys. B 682 618
[22] Blo ̈te H W J, Luijiten E and Heringa J R 1995 J. Phys. A: Math. Gen. 28 6289 [23] Henkel M and Schutz G 1988 J. Phys. A: Math. Gen. 21 2617

50

arXiv:cond-mat/0703199 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi 10.1143/JPSJ.76.074711
Inequalities for the Local Energy of Random Ising Models
Authors: Hidetsugu Kitatani, Hidetoshi Nishimori, Akira Aoki
Submitted 8 March, 2007; originally announced March 2007.
Comments: 10 pages. Submitted to J. Phys. Soc. Jpn
https://arxiv.org/abs/cond-mat/0703199

H. Nishimori: Statistical Physics of Spin Glasses and Information Processing: An Introduction, Oxford University Press (Oxford, 2001).
M. M ́ezard, G. Parisi and M. A. Virasoro: Spin Glass Theory and Beyond, World Scientific (Sin- gapore, 1987).
H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169.
P. Contucci and S. Graffi: J. Stat. Phys. 115 (2004) 581.
P. Contucci and S. Graffi: Commun. Math. Phys. 248 (2004) 207.
P. Contucci, S. Morita and H. Nishimori: J. Stat. Phys. 122 (2006) 303.
S. Morita, H. Nishimori and P. Contucci: J. Phys. A: Math. Gen. 37 (2004) L203.
P. Contucci and J. L. Lebowitz: cond-mat/0612371.
H. Nishimori: J. Phys. Soc. Jpn. 62 (1993) 2973.
R. B. Griffiths: J. Math. Phys. 8 (1967) 478, 484.

51

arXiv:quant-ph/0702252 [pdf, ps, other] quant-ph cond-mat.dis-nn
doi
10.1143/JPSJ.76.064002
Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics
Authors: Satoshi Morita, Hidetoshi Nishimori
Submitted 25 May, 2007; v1 submitted 27 February, 2007; originally announced February 2007.
Comments: 6 pages, minor corrections
Journal ref: J. Phys. Soc. Jpn. 76 (2007) 064002
https://arxiv.org/abs/quant-ph/0702252

T. Kadowaki and H. Nishimori: Phys. Rev. E 58 (1998) 5355.
A. Das and B. K. Chakrabarti: Quantum Annealing and Related Optimization Methods (Lecture
Notes in Physics 679) (Springer, Berlin Heidelberg, 2005).
G. E. Santoro and E. Tosatti: J. Phys. A: Math. Gen. 39 (2006) R393.
A. B. Finnila, M. A. Gomez, D. Sebenik, C. Stenson and J. D. Doll: Chem. Phys. Lett. 219 (1994)
E. Farhi, J. Goldstone, S. Gutmann and M. Sipser: quant-ph/0001106.
G. E. Santoro, R. Martonˇa ́k, E. Tosatti and R. Car: Science 295 (2002) 2427.
R. Martonˇa ́k, G. E. Santoro and E. Tosatti: Phys. Rev. B 66 (2002) 094203.
S. Suzuki and M. Okada: J. Phys. Soc. Jpn 74 (2005) 1649.
M. Sarjala, V. Pet ̈aja ̈ and M. Alava: J. Stat. Mech. (2006) P01008.
Y-H. Lee and B. J. Berne: J. Phys. Chem. A 104 (2000) 86.
P. Liu and B. J. Berne: J. Chem. Phys. 118 (2003) 2999.
R. Martonˇa ́k, G. E. Santoro and E. Tosatti: Phys. Rev. E 70 (2004) 057701.
L. Stella, G. E. Santoro and E. Tosatti: Phys. Rev. B 72 (2005) 014303.
L. Stella, G. E. Santoro and E. Tosatti: Phys. Rev. B 73 (2006) 144302.
A. Das, B. K. Chakrabarti and R. B. Stinchcombe: Phys. Rev. E 72 (2005) 026701.
S. Kirkpatrick, S. D. Gelett and M. P. Vecchi: Science 220 (1983) 671.
E. Aarts and J. Korst: Simulated Annealing and Boltzmann Machines: a Stochastic Approach to
Combinatorial Optimization and Neural Computing (Wiley, New York, 1989) Chap. 3, p. 33.
S. Morita and H. Nishimori: J. Phys. A: Math. Gen. 39 (2006) 13903.
S. Geman and D. Geman: IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6 (1984) 721.
R. D. Somma, C. D. Batista and G. Ortiz: quant-ph/0609216.
A. Messiah: Quantum Mechanics (Wiley, New York, 1976).
E. Hopf: J. Math. Mech. 12 (1963) 683.
S. Suzuki, H. Nishimori and M. Suzuki: quant-ph/0702214.

52

arXiv:quant-ph/0702214 [pdf, ps, other] quant-ph cond-mat.dis-nn cond-mat.stat-mech
doi 10.1103/PhysRevE.75.051112
Quantum annealing of the random-field Ising model by transverse ferromagnetic interactions
Authors: Sei Suzuki, Hidetoshi Nishimori, Masuo Suzuki
Submitted 23 February, 2007; originally announced February 2007.
Comments: 6 pages, 9 figures
Journal ref: Phys. Rev. E 75, 051112 (2007)
https://arxiv.org/abs/quant-ph/0702214

[1] M. R. Garey and D. S. Johnson, Computers and In- trectability: A Guide to the Theory of NP-Completeness, (Freeman, San Francisco, 1979).
[2] J. J. Hopfield and D. W. Tank, Science 233 625 (1986).
[3] S. Kirkpatrick, C. D. Gelett, and M. P. Vecchi, Science 220, 671 (1983).
[4] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[5] Quantum Annealing and Related Optimization Methods, Eds. A. Das and B. K. Chakrabarti (Springer, Heidelberg, 2005).
[6] G. E. Santoro and E. Tosatti, J. Phys. A: Math. Gen. 39 R393 (2006).
[7] A. B. Finnila, M. A. Gomez, C. Sebenik, C. Stenson, and J. D. Doll, Chem. Phys. Lett. 219, 343 (1994).
[8] T. Kadowaki, Ph.D. thesis, Tokyo Institute of Technology, 1998; quant-ph/0205020(unpublished).
[9] R. Martonˇ ́ak, G. E. Santoro, and E. Tosatti, Phys. Rev. B 66, 94203 (2002).
[10] L. Stella and G. E. Santoro, cond-mat/0608420.
[11] G.E.Santoro,R.Martonˇ ́ak,E.Tosatti,andR.Car, Science 295, 2427 (2002).
[12] R. Martonˇ ́ak, G. E. Santoro, and E. Tosatti, Phys. Rev. E 70, 057701 (2004).
[13] M. Sarjala, V. Pet ̈aja ̈, and M. Alava, J. Stat. Mech., 1008 (2006).
[14] E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, quant-ph/0001106.
[15] S. Suzuki and M. Okada, J. Phys. Soc. Jpn. 74, 1649 (2005).
[16] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976). See also Quantum Monte Carlo Methods in Condensed Matter Physics, ed. M. Suzuki (World Scientific, 1993), and ref- erences cited therein.
[17] Mean-field annealing with the simplest Weiss-type ap- proximiation for quantum systems has been first dis- cussed in K. Tanaka and T. Horiguchi, Electron. Com- mun. Jpn. Pt. 3 83 84 (2000).
[18] M. Alava, P. Duxbury, C. Moukarzel, and H. Rieger, Phase Transitions and Critial Phenomena vol. 18, eds. C. Domb and J. L. Lobowitz (2001, San Diego, CA: Aca- demic).
[19] D. A. Battaglia, G. E. Santoro, and E. Tosatti, Phys. Rev. E 71 66707 (2005).

53

arXiv:cond-mat/0611168 [pdf, ps, other] cond-mat.dis-nn
doi 10.1143/JPSJ.76.054002
Phase diagram of the p-spin-interacting spin glass with ferromagnetic bias and a transverse field in the infinite-p limit
Authors: Tomoyuki Obuchi, Hidetoshi Nishimori, David Sherrington
Submitted 22 March, 2007; v1 submitted 6 November, 2006; originally announced November 2006.
Comments: 16 pages, 4 figures. another additional author, some amendments
Journal ref: J. Phys. Soc. Jpn. 76 (2007) 054002
https://arxiv.org/abs/cond-mat/0611168

H. Nishimori: Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford University Press, Oxford, 2001)
M. M ́ezard, G. Parisi, and M. A. Virasoro: Spin Glass Theory and Beyond (World Scientific, Sin- gapore, 1987)
A. J. Bray and M. A. Moore: J. Phys. C 13 (1980) L665.
H. Ishii and T. Yamamoto: J. Phys. C 18 (1985) 6225.
D. Thirumalai, Q. Li and T. R. Kirkpatrick: J. Phys. A 22 (1989) 3339.
G. Bu ̈ttner and K. D. Usadel: Phys. Rev. B 41 (1990) 428.
Y. Y. Goldschmidt: Phys. Rev. B 41 (1989) 4858.
M. Suzuki: Prog. Theor. Phys. 56 (1976) 1454.
D. Sherrigton and S. Kirkpatrick: Phys. Rev. Lett. 35 (1975) 1792.
B. Derrida: Phys. Rev. B 24 (1981) 2613.
V. Dobrosavljevic and D. Thirumalai: J. Phys. A 23 (1990) L767.
D. J. Gross and M. M ́ezard: Nucl. Phys. B240 (1984) 431.
N. Sourlas: Nature 339 (1989) 693.
H. Nishimori and Y. Nonomura: J. Phys. Soc. Jpn. 65 (1996) 3780.
L. De Cesare, K. Lukierska-Walasek, I. Rabuffo and K. Walasek: J. Phys. A 29 (1996) 1605.
E. Gardner: Nucl. Phys. B257 (1985) 747.
P. Gillin, H. Nishimori and D. Sherrington: J. Phys. A 34 (2001) 2949.
D. B. Saakyan: Teoreticheskaya Mathematicheskaya Fizika 94 (1993) 173.
J. Inoue: in Quantum Annealing and Related optimization Methods, Lect. Notes Phys. 679, ed. A.
Das and B. K. Chakrabarti (Springer, Berlin Heidelberg, 2005)p. 259.

54

arXiv:quant-ph/0608154 [pdf, ps, other] quant-ph cond-mat.dis-nn cond-mat.stat-mech
doi 10.1088/0305-4470/39/45/004
Convergence theorems for quantum annealing
Authors: Satoshi Morita, Hidetoshi Nishimori
Submitted 21 August, 2006; originally announced August 2006.
Comments: 19 pages
Journal ref: J. Phys. A: Math. Gen. 39 (2006) 13903
https://arxiv.org/abs/quant-ph/0608154

[1] Garey M R and Johnson D S 1979 Computers and Intractability: A Guide to the Theory of NP Completeness (San Francisco: Freeman)
[2] Kirkpatrick S, Gelett S D and Vecchi M P 1983 Science 220 671
[3] Aarts E and Korst J 1984 Simulated Annealing and Boltzmann Machines: a Stochastic Approach
to Combinatorial Optimization and Neural Computing (New York: Wiley) ch 3
[4] Geman S and Geman D 1984 IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6 721
[5] Amara P, Hsu D and Atraub J E 1993 J. Phys. Chem. 97 6715
[6] Finnila A B, Gomez M A, Sebenik C, Stenson C and Doll J D 1994 Chem. Phys. Lett. 219 343 [7] Tanaka K and Horiguchi H 1997 Trans. Inst. Electron. Inform. Commun. Eng. J80 2117 (in Japanese); Tanaka K and Horiguchi H 2000 Electron. Commun. Jpn. Pt. 3 83 84 (English translation)
[8] Kadowaki T and Nishimori H 1998 Phys. Rev. E 58 5355
[9] Kadowaki T 1999 Thesis (Tokyo Institute of Technology) quant-ph/0205020
[10] Das A and Chakrabarti B K (eds) 2005 Quantum Annealing and Related Optimization Methods (Lecture Notes in Physics 679) (Berlin Heidelberg: Springer)
[11] Fahhi E, Goldstone J, Gutmann S and Sipser M 2000 quant-ph/0001106 [12] Santoro G E, Martonˇak R, Tosatti E and Car R 2002 Science 295 2427 [13] Martonˇak R, Santoro G E and Tosatti E 2002 Phys. Rev. E 66 094203 [14] Sarjala M, Pet ̈aja ̈ V and Alava M 2006 J. Stat. Mech. P01008
[15] Suzuki S and Okada M 2005 J. Phys. Soc. Jpn 74 1649
[16] Lee Y-H and Berne B J 2000 J. Phys. Chem. A 104 86
[17] Liu P and Berne B J 2003 J. Chem. Phys. 118 2999
[18] Martonˇa`k R, Santoro G E and Tosatti E 2004 Phys. Rev. E 70 057701 [19] Stella L, Santoro G E and Tosatti E 2005 Phys. Rev. B 72 014303
[20] Stella L, Santoro G E and Tosatti E 2006 Phys. Rev. E 73 144302
[21] Das A, Chakrabarti B K and Stinchcombe R B 2005 Phys. Rev. E 72 026701
[22] Brooke J, Bitko D, Rosenbaum T F and Aeppli G 1999 Science 284 779
[23] Battaglia D A, Santoro G E and Tosatti E 2005 Phys. Rev. E 71 066707
[24] Landau D P and Binder K 2000 A Guide to Monte Carlo Simulations in Statistical Physics
(Cambridge: Cambridge University Press) ch 8
[25] Trotter H F 1959 Proc. Am. Math. Soc. 10 545
[26] Suzuki M 1971 Prog. Theor. Phys. 46 1337
[27] Nishimori H and Inoue J 1998 J. Phys. A: Math. Gen. 31 5661 [28] Tsallis C and Stariolo D A 1996 Physica 233A 395
[29] Ceperley D M and Alder B J 1980 Phys. Rev. Lett. 45 566
[30] Trivedi N and Ceperley D M 1990 Phys. Rev. B 41 4552
[31] Stella L, Santoro G E and Tosatti E 2005 Phys. Rev. B 72 014303

55

arXiv:cond-mat/0605688 [pdf, ps, other] cond-mat.stat-mech
doi 10.1143/JPSJ.75.114003
Internal Energy of the Potts model on the Triangular Lattice with Two- and Three-body Interactions
Authors: Masayuki Ohzeki, Hidetoshi Nishimori
Submitted 14 November, 2006; v1 submitted 28 May, 2006; originally announced May 2006.
Comments: 9 pages, 4 figures
Journal ref: J. Phys. Soc. Jpn. Vol. 75,(2006)114003
https://arxiv.org/abs/cond-mat/0605688

H. A. Kramers and G. H. Wannier: Phys. Rev. 60 (1941) 252.
R. B. Potts: Proc. Camb. Phil. Soc. 48 (1952) 106.
T. Kihara, Y. Midzuno, and T. Shizume: J. Phys. Soc. Jpn. 9 (1954) 681.
D. Kim and R. I. Joseph: J. Phys. C: Solid State Phys. 7 (1974) L167.
I. Syozi: in Phase transition and Critical Phenomena, Vol. 1, Eds. C. Domb and M. S. Green
(Academic Press, 1972).
R. J. Baxter, H. N. V. Temperly and S. E. Ashley: Proc. R. Soc. A358 (1978) 535.
F. Y. Wu and K. Y. Lin: J. Phys. A: Math. Gen. 13 (1980) 629.
F. Y. Wu: Rev. Mod. Phys. 54 (1982) 235.
M. Schick and R. B. Griffiths: J. Phys. A: Math. Gen. 10 (1977) 2123.
F. Y. Wu and R. K. P. Zia: J. Phys. A: Math. Gen. 14 (1981) 721.

56

arXiv:cond-mat/0602453 [pdf, ps, other] cond-mat.dis-nn math-ph
doi 10.1007/s10955-006-9156-1
Duality in finite-dimensional spin glasses
Authors: Hidetoshi Nishimori
Submitted 6 June, 2006; v1 submitted 20 February, 2006; originally announced February 2006.
Comments: 12 pages, 3 figures; A reference added; to appear in J. Stat. Phys
Journal ref: J. Stat. Phys. 126 (2007) 977
https://arxiv.org/abs/cond-mat/0602453

[1] D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).
[2] M. M ́ezard, G. Parisi and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
[3] F. Guerra, Commun. Math. Phys. 233, 1 (2003).
[4] M. Talagrand, (this issue).
[5] A. P. Young (ed), Spin Glasses and Random Fields (World Scientific, Singapore, 1997).
[6] H. Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford, Oxford, 2001).
[7] C. W. Newman and D. L. Stein, (this issue).
[8] H. Nishimori and K. Nemoto, J. Phys. Soc. Jpn. 71, 1198 (2002).
[9] J.-M. Maillard, K. Nemoto and H. Nishimori J. Phys. A36, 9799 (2003).
[10] K. Takeda and H. Nishimori, Nucl. Phys. B686, 377 (2004).
[11] K. Takeda, T. Sasamoto and H. Nishimori, J. Phys. A38, 3751 (2005).
[12] H. Nishimori and M. Ohzeki, J. Phys. Soc. Jpn. 75, 034004 (2006).
[13] F. Y. Wu and Y. K. Wang, J. Math. Phys. 17, 439 (1976).
[14] P. Le Doussal and A. B. Harris, Phys. Rev. B40, 9249 (1989).
[15] S. L. A. de Queiroz, Phys. Rev. B73, 064410 (2006).
[16] N. Ito and Y. Ozeki, Physica A321, 262 (2003).
[17] F. Merz and J. T. Chalker, Phys. Rev. B65, 054425 (2002).
[18] A. Honecker, M. Picco and P. Pujol, Phys. Rev. Lett. 87, 047201 (2001).
[19] F. D. A. Aar ̃ao Reis, S. L. A. de Queiroz and R. R. dos Santos, Phys. Rev. B60, 6740 (1999).
[20] Y. Ozeki, (private communication)
[21] J. L. Jacobsen and M. Picco, Phys. Rev. E65, 026113 (2002).
[22] G. Arakawa, I. Ichinose, T. Matsui and K. Takeda, Nucl. Phys. B709, 296 (2005).
[23] Y. Ozeki and N. Ito, J. Phys. A31, 5451 (1998).
[24] T. Ohno, G. Arakawa, I. Ichinose and T. Matsui, Nucl. Phys. B697, 462 (2004); C. Wang, J. Harrington and J. Preskill, Ann. Phys. 303, 31 (2003).
[25] M. Hinczewski and A. N. Berker, Phys. Rev. B72, 144402 (2005).
[26] F. D. Nobre, Phys. Rev. E64, 046108 (2001).
[27] I. A. Gruzberg, N. Read and A. W. W. Ludwig, Phys. Rev. 63, 104422 (2001).

57

arXiv:cond-mat/0601356 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi 10.1143/JPSJ.75.034004
Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices
Authors: Hidetoshi Nishimori, Masayuki Ohzeki
Submitted 9 March, 2006; v1 submitted 16 January, 2006; originally announced January 2006.
Comments: 9 pages, 1 figure; Minor corrections in notation
Journal ref: J. Phys. Soc. Jpn. 75 (2006) 034004
https://arxiv.org/abs/cond-mat/0601356

S. F. Edwards and P. W. Anderson: J. Phys. F 5 (1975) 965.
D. Sherrington and S. Kirkpatrick: Phys. Rev. Lett. 35 (1975) 1792.
A. P. Young (ed): Spin Glasses and Random Fields (World Scientific, Singapore, 1997).
H. Nishimori and K. Nemoto: J. Phys. Soc. Jpn. 71 (2002) 1198.
J.-M. Maillard, K. Nemoto and H. Nishimori: J. Phys. A 36 (2003) 9799.
K. Takeda and H. Nishimori: Nucl. Phys. B 686 (2004) 377.
K. Takeda, T. Sasamoto and H. Nishimori: J. Phys. A 38 (2005) 3751.
F. Y. Wu: Rev. Mod. Phys. 54 (1982) 325.
H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169.
H. Nishimori: Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford Univ. Press, Oxford, 2001).
S. L. A. de Queiroz: Phys. Rev. B 73 (2006) 064410.

58

arXiv:cond-mat/0508511 [pdf, ps, other] cond-mat.dis-nn
doi
10.1143/JPSJ.75.014001
Gauge Theory for Quantum Spin Glasses
Authors: Satoshi Morita, Yukiyasu Ozeki, Hidetoshi Nishimori
Submitted 22 August, 2005; originally announced August 2005.
Comments: 15 pages, 2 figures
Journal ref: J. Phys. Soc. Jpn. 75 (2006) 014001
https://arxiv.org/abs/cond-mat/0508511

K. Binder and A. P. Young: Rev. Mod. Phys. 58 (1986) 801.
K. H. Fischer and J. A. Hertz: Spin Glasses (Cambridge University Press, Cambridge, 1991).
S. F. Edwards and P. W. Anderson: J. Phys. F 5 (1975) 965.
D. Sherrington and S. Kirkpatrick: Phys. Rev. Lett. 35 (1975) 1972.
G. Parisi: Phys. Lett. 73A (1979) 203, J. Phys. A 13 (1980) 1011, 1887 and L115.
R. N. Bhatt and A. P. Young: Phys. Rev. Lett. 54 (1985) 924.
A. T. Ogielski and I. Morgenstern: Phys. Rev. Lett. 54 (1985) 928.
R. R. P. Singh and S. Chakravarty: Phys. Rev. Lett. 57 (1986) 245.
R. N. Bhatt and A. P. Young: Phys. Rev. B 37 (1988) 5606.
D. A. Huse and H. S. Seung: Phys. Rev. B 42 (1990) 1059.
J. D. Reger, T. A. Tokuyasu, A. P. Young and M. P. A. Fisher: Phys. Rev. B 44 (1991) 7147.
M. Cieplak, J. R. Banavar and A. Khaurana: J. Phys. A 24 (1991) L145.
J. M. Kosterlitz and M. V. Simkin: Phys. Rev. B 79 (1997) 1098.
H. Nishimori and H. Kawamura: J. Phys. Soc. Jpn. 62 (1993) 3266.
M. J. P. Gingras: Phys. Rev. B 45 (1992) 7547.
J. D. Reger and A. P. Young: J. Phys. A 26 (1993) L1067.
Y-H. Lie: Phys. Rev. Lett. 69 (1992) 1819.
M. Y. Choi and S. Y. Park: Phys. Rev. B 60 (1999) 4070.
H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169.
H. Nishimori: Statistical Physics on Spin Glasses and Information Processing: An Introduction
(Oxford University Press, Oxford, 2001).
H. Kitatani: J. Phys. Soc. Jpn 61 (1992) 4049.
Y. Ozeki and H. Nishimori: J. Phys. A 26 (1993) 3399.
Y. Ozeki: J. Phys. A 28 (1995) 3645, J. Phys. Condens. Matter 9 (1997) 11171.
Y. Ozeki: J. Phys. A 36 (2003) 2673.
J. M. Kosterlitz and D. J. Thouless: J. Phys. C 6 (1973) 1181.
T. Kennedy, E. H. Lieb, and B. S. Shastry: Phys. Rev. Lett. 61 (1988) 2582.
Y. Ozeki: J. Phys. A 29 (1996) 5805.

#59
arXiv:math-ph/0503023 [pdf, ps, other] math-ph cond-mat.dis-nn
doi
10.1007/s10955-005-8020-z
Surface terms on the Nishimori line of the Gaussian Edwards-Anderson model
Authors: Pierluigi Contucci, Satoshi Morita, Hidetoshi Nishimori
Submitted 7 June, 2005; v1 submitted 10 March, 2005; originally announced March 2005.
Comments: Final version with minor corrections. To appear in Journal of Statistical Physics
https://arxiv.org/abs/math-ph/0503023

[FL] M. E. Fisher and J. L. Lebowitz, Commun. Math. Phys., 19, 251-272, (1970).
[G] F. Guerra, Phys. Rev. Lett., 28, 1213-1215, (1972)
[GRS] F. Guerra, L. Rosen and B. Simon, Ann. Inst. H. Poincare, A25, 231-334, (1976).
[FC] M. E. Fisher and G. Caginalp, Commun. Math. Phys., 56, 11-56, (1977)
[CG1] P. Contucci and S. Graffi, Jou. Stat. Phys., 115, 581-589,(2004)
[CG2] P. Contucci and S. Graffi, Commun. Math. Phys., 248, 207-216, (2004)
[GT] F. Guerra and F. Toninelli, Commun. Math. Phys., 230, 71-79 (2002)
[G2] F. Guerra, Commun. Math. Phys., 233, 1-12 (2003)
[N] H. Nishimori, Prog. Theor., 66 1169-1181 (1981)
[N2] H. Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction, Oxford: Oxford University Press, (2001)
[CF] G. Caginalp and M. E. Fisher, Commun. Math. Phys., 65, 247-280, (1979)
[MNC] S. Morita, H. Nishimori and P. Contucci, Jou. Phys. A: Math. and Gen., 37, L203-L209, (2004)
[Gr] R. B. Griffiths, Jou. Math. Phys., 8, 478-483, 484-489, (1967)
[Si] B. Simon, The statistical mechanics of lattice gases, Princeton Univ. Press, (1992)

60

arXiv:cond-mat/0501372 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech hep-th quant-ph
doi 10.1088/0305-4470/38/17/004
Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture
Authors: Koujin Takeda, Tomohiro Sasamoto, Hidetoshi Nishimori
Submitted 17 January, 2005; originally announced January 2005.
Comments: 27 pages, 3 figures
Journal ref: J.Phys. A38 (2005) 3751-3774
https://arxiv.org/abs/cond-mat/0501372

[1] M ́ezard M, Parisi G and Virasoro M A 1986 Spin glass theory and beyond (World Scientific); Young A P (ed) 1997 Spin glasses and random fields (World Scientific); Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An introduction (Oxford)
[2] Nishimori H and Nemoto K 2002 J. Phys. Soc. Japan 71 1198
[3] Maillard J -M, Nemoto K and Nishimori H 2003 J. Phys. A: Math. Gen. 36 9799 [4] Takeda K and Nishimori H 2004 Nucl. Phys. B 686 377
[5] Wegner F 1971 J. Math. Phys. 12 2259
[6] Wu F and Wang Y 1976 J. Math. Phys. 17 439
[7] Nishimori H 1981 Prog. Theor. Phys. 66 1169 Exact location of the multicritical point: A conjecture 27
[8] Singh R R P and Adler J 1996 Phys. Rev. B 54 364; Aarao Reis F D A, de Queiroz S L A and dos Santos R R 1999 Phys. Rev. B 60 6740; Honecker A, Picco M and Pujol P 2001 Phys. Rev. Lett. 87 047201; Merz F and Chalker J T 2002 Phys. Rev. B 65 054425; Ito N and Ozeki Y 2003 Physica A 321 262; de Queiroz S L A and Stinchcombe R 2003 Phys. Rev. B 68 144414
[9] Arakawa G, Ichinose I, Matsui T and Takeda K Preprint hep-th/0409076, to appear in Nucl. Phys. B
[10] Kitaev A 2003 Ann. Phys., NY 303 2
[11] Dennis E, Kitaev A, Landahl A and Preskill J 2002 J. Math. Phys. 43 4452; Wang C, Harrington J and Preskill J 2003 Ann. Phys., NY 303 31
[12] See e.g. Itzykson C and Drouffe J -M 1989 Statistical field theory vol. I (Cambridge)
[13] Ito N 1993 Physica A 192 604; Ito N 1993 Physica A 196 591; Ito N, Matsuhisa T and Kitatani H 1998 J. Phys. Soc. Japan 67 1188; Ozeki Y and Ito N 1998 J. Phys. A: Math. Gen. 31 5451
[14] Ito N, Ozeki Y and Kitatani H 1999 J. Phys. Soc. Japan 68 803
[15] Ohno T, Arakawa G, Ichinose I and Matsui T 2004 Nucl. Phys. B 697 462
[16] Jos ́e J V, Kadanoff L P, Kirkpatrick S and Nelson D R 1977 Phys. Rev. B 16 1217
[17] Elitzur S, Pearson R B and Shigemitsu J 1979 Phys. Rev. D 19 3698
[18] Villain J 1975 J. Physique 36 581
[19] Ozeki Y and Nishimori H 1993 J. Phys. A: Math. Gen. 26 3399
[20] Korshunov S E 1993 Phys. Rev. B 48 1124
[21] Tang L -H 1996 Phys. Rev. B 54 3350
[22] Mudry C and Wen X -G 1999 Nucl. Phys. B 549 613
[23] Griffiths R B 1964 Phys. Rev. 136 A437
[24] Horiguchi T and Morita T 1982 J. Phys. A: Math. Gen. 15 L75
[25] Horiguchi T and Morita T 1981 J. Phys. A: Math. Gen. 14 2715
[26] Horiguchi T and Morita T 1979 Phys. Lett. A 74 340
[27] Ozeki Y work in progress
[28] Holme P, Kim B J and Minnhagen P 2003 Phys. Rev. B 67 104510

61

arXiv:cond-mat/0410694 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
Possibly Exact Solution for the Multicritical Point of Finite-Dimensional Spin Glasses
Authors: Hidetoshi Nishimori, Koujin Takeda, Tomohiro Sasamoto
Submitted 27 October, 2004; originally announced October 2004.
Comments: Proceedings for the Recent Progress in Many-Body Theories XII (Santa Fe, US, August 2004)
https://arxiv.org/abs/cond-mat/0410694

[1] S. F. Edwards and P. W. Anderson, J. Phys. F5, 965 (1975).
[2] D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).
[3] G. Parisi, J. Phys. A13, L115, 1101, 1887 (1983).
[4] H. Nishimori, Statistical Physics of Spin Glasses and Information Processing – An Introduction (Oxford, Oxford, 2001).
[5] H. Nishimori and K. Nemoto, J. Phys. Soc. Jpn. 71, 1198 (2002).
[6] J.-M. Maillard, K. Nemoto and H. Nishimori J. Phys. A36, 9799 (2003).
[7] K. Takeda and H. Nishimori, Nucl. Phys. B686, 377 (2004).
[8] K. Takeda, T. Sasamoto and H. Nishimori, (in preparation).8
[9] N. Ito and Y. Ozeki, Physica A321, 262 (2003).
[10] Y. Ozeki, (private communication)
[11] A. Honecker, M. Pico and P. Pujol, Phys. Rev. Lett. 87, 047201 (2001).
[12] G. Arakawa, I. Ichinose, T. Matsui and K. Takeda, hep-th/0409076.
[13] Y. Ozeki and N. Ito, J. Phys. A31, 5451 (1998).
[14] T. Ohno, G. Arakawa, I. Ichinose and T. Matsui, Nucl. Phys. B697, 462 (2004); C. Wang, J. Harrington and J. Preskill, Ann. Phys. 303, 31 (2003).
[15] J. V. Jos ́e, L. P. Kadanoff, S. Kirkpatrick and D. R. Nelson, Phys. Rev. B16, 1217 (1977).
[16] T. Shirakura and F. Matsubara, J. Phys. Soc. Jpn. 65, 3138 (1996); F. Matsubara, T. Shirakura and M. Shiomi, Phys. Rev. B58, R11821 (1998).
[17] P. Holme, B. J. Kim and P. Minnhagen, Phys. Rev. B67, 104510 (2003).

62

arXiv:cond-mat/0405313 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech quant-ph
doi 10.1143/JPSJ.73.2701
Error counting in a quantum error-correcting code and the ground-state energy of a spin glass
Authors: Hidetoshi Nishimori, Peter Sollich
Submitted 14 May, 2004; originally announced May 2004.
Comments: 15 pages, 7 figures, JPSJ style, latex style file included
Journal ref: Journal of the Physical Society of Japan, 73:2701-2707, 2004
https://arxiv.org/abs/cond-mat/0405313

E. Dennis, A. Kitaev, A. Landahl and J. Preskill: J. Math. Phys. 43 (2002) 4452.
J.-M. Maillard, K. Nemoto and H. Nishimori: J. Phys. A 36 (2003) 9799.
H. Nishimori and K. Nemoto, J. Phys. Soc. Jpn. 71 (2002) 1198.
A. R. Calderbank and P. W. Shor: Phys. Rev. A 54 (1996) 1098.
A. Steane: Proc. R. Soc. London A 452 (1996) 2551.
H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169.
H. Nishimori: Statistical Physics of Spin Glasses and Information Processing: An Introduction
(Oxford University Press, Oxford, 2001).
H. Nishimori and P. Sollich: J. Phys. Soc. Jpn. 69 (2000) Supple. A 160.
H. Nishimori: J. Phys. Soc. Jpn. 55 (1986) 3305.
The Spin Glass Ground State Server: http://www.informatik.uni- koeln.de/ls juenger/research/sgs/sgs.html.

63

arXiv:cond-mat/0403625 [pdf, ps, other] cond-mat.dis-nn math-ph
doi 10.1088/0305-4470/37/18/L03
Griffiths inequalities for the Gaussian spin glass
Authors: Satoshi Morita, Hidetoshi Nishimori, Pierluigi Contucci
Submitted 30 April, 2004; v1 submitted 24 March, 2004; originally announced March 2004.
Comments: 8 pages; Added references
Journal ref: J. Phys. A 37 (2004) L203
https://arxiv.org/abs/cond-mat/0403625

[1] Griffiths R B 1972 Phase Transitions and Critical Phenomena vol 1 ed, C Domb and M S Green (London: Academic) p 7
[2] Griffiths R B 1967 J. Math. Phys 8 478, 484
[3] Guerra F and Toninelli F 2002 Commun. Math. Phys. 230 71
[4] Contucci P and Graffi S 2003 Preprint math-ph/0306006 (Commun. Math. Phys at press)
[5] Contucci P and Graffi S 2004 J. Stat. Phy. 115 581
[6] Nishimori H 1981 Prog. Theor. Phys, 66 1169
[7] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction
(Oxford: Oxford University Press)
[8] Kitatani H 1994 J. Phys. Soc. Jpn. 63 2070

64

arXiv:cond-mat/0403038 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi 10.1143/PTPS.157.120
Exact Ground-State Energies of the Random-Field Ising Chain and Ladder
Authors: Toshiyuki Hamasaki, Hidetoshi Nishimori
Submitted 1 March, 2004; originally announced March 2004.
Comments: 15 pages, 3 figures
Journal ref: J. Phys. Soc. Jpn. 73 (2004) 1490-1495
https://arxiv.org/abs/cond-mat/0403038

B. Derrida, J. Vannimenus and Y. Pomeau: J. Phys. C 11 (1978) 4749.
E. Farhi and S. Gutmann: Phys. Rev. B 48 (1993) 9508.
A. Vilenkin: Phys. Rev. B 18 (1978) 1474.
C. Dress, E. Amic and J. M. Luck: J. Phys. A: Math. Gen. 28 (1995) 135.
T. Kadowaki,Y. Nonomura and H. Nishimori: J. Phys. Soc. Jpn. 65 (1996) 1609. 6) P. Shukla: Physica A 233 (1996) 235.
P. Shukla: Phys. Rev. E 62 (2000) 4725.
L. Dante, G. Durin, A. Magni and S. Zapperi: Phys. Rev. B 65 (2002) 144441. 9) P. Rujan: Phys. Rev. Lett 70 (1993) 2968.

65

arXiv:hep-th/0310279 [pdf, ps, other] hep-th cond-mat.dis-nn quant-ph
doi 10.1016/j.nuclphysb.2004.03.006
Self-dual random-plaquette gauge model and the quantum toric code
Authors: Koujin Takeda, Hidetoshi Nishimori
Submitted 7 May, 2004; v1 submitted 30 October, 2003; originally announced October 2003.
Comments: 23 pages, 13 figures
Journal ref: Nucl. Phys. B686 (2004) 377-396
https://arxiv.org/abs/hep-th/0310279

[1] See e.g. C. Itzykson and J. -M. Drouffe, Statistical Field Theory (Cambridge University Press, Cambridge, 1989) and references therein.
[2] A. Yu. Kitaev, “Quantum error correction with imperfect gates” in Proceedings of the Third International Conference on Quantum Communication and Measurement, edited by O. Hirota,A. S. Holevo and C. M. Caves (Plenum, New York, 1997); A. Yu. Kitaev, Ann. Phys. 303 (2003) 2.
[3] E. Dennis, A. Kitaev, A. Landahl and J. Preskill, J. Math. Phys. 43 (2002) 4452.
[4] C. Wang, J. Harrington and J. Preskill, Ann. Phys. 303 (2003) 31;
Recently new results are obtained for 3D RPGM: G. Arakawa, I. Ichinose, Ann. Phys. 311 (2004) 152; T. Ohno, G. Arakawa, I. Ichinose, T. Matsui, quant-ph/0401101.
[5] H. Nishimori, Prog. Theor. Phys. 66 (1981) 1169; H. Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford University Press, Oxford, 2001).
[6] F. J. Wegner, J. Math. Phys. 12 (1971) 2259; R. Balian, J. M. Drouffe and C. Itzykson, Phys. Rev. D11 (1975) 2098; C. P. Korthals Altes, Nucl. Phys. B142 (1978) 315; A. Ukawa, P. Windey and A. H. Guth, Phys. Rev. D21 (1980) 1013.
[7] F. Y. Wu and Y. K. Wang, J. Math. Phys. 17 (1976) 439.
[8] J. -M. Maillard, K. Nemoto and H. Nishimori, J. Phys. A36 (2003) 9799; H. Nishimori and K.
Nemoto, J. Phys. Soc. Jpn. 71 (2002) 1198.
[9] R. R. P. Singh and J. Adler, Phys. Rev. B54 (1996) 364; F. D. A. Aarao Reis, S. L. A. de Queiroz and R. R. dos Santos, Phys. Rev. B60 (1999) 6740; A. Honecker, M. Picco and P. Pujol, Phys. Rev. Lett. 87 (2001) 047201; F. Merz and J. T. Chalker, Phys. Rev. B65 (2002) 054425; N. Ito and Y. Ozeki, Physica A321 (2003) 262; S. L. A. de Queiroz and R. Stinchcombe, Phys. Rev. B68 (2003) 144414.
[10] See e.g. R. B. Griffiths, “Rigorous Results and Theorems” in Phase Transition and Critical Phenomena, Vol. 1, edited by C. Domb and M. S. Green (Academic Press, London, 1972).
[11] For resent results, see e.g. H. W. J. Blo ̈te, L. N. Shchur and A. L. Talapov, Int. J. Mod. Phys. C10 (1999) 1137; N. Ito, S. Fukushima, H. Watanabe and Y. Ozeki, ”Recent Development in Nonequilibrium Relaxation Method” in Computer Simulation Studies in Condensed-Matter Physics XIV, edited by D. P. Landau, S. P. Lewis and H. -B. Schuu ̈ttler (Springer-Verlag, Berlin, 2002); H. Arisue and T. Fujiwara, Nucl. Phys. B (Proc. Suppl.) 119 (2003) 855; Phys. Rev. E67 (2003) 066109.

66

arXiv:cond-mat/0306154 [pdf, ps, other] cond-mat.stat-mech cond-mat.dis-nn
doi 10.1088/0305-4470/36/38/301
Symmetry, complexity and multicritical point of the two-dimensional spin glass
Authors: Jean-Marie Maillard, Koji Nemoto, Hidetoshi Nishimori
Submitted 5 August, 2003; v1 submitted 5 June, 2003; originally announced June 2003.
Comments: 32 pages, 6 figures; a few typos corrected. To be published in J. Phys. A
Journal ref: J. Phys. A 36 (2003) 9799
https://arxiv.org/abs/cond-mat/0306154

[1] M ́ezard M, Parisi G and Virasoro M A 1987 Spin Glass Theory and Beyond (World Scientific: Singapore)
[2] Young A P (Ed) 1997 Spin Glasses and Random Fields (World Scientific: Singapore)
[3] Nishimori H 1981 Prog. Theor. Phys. 66 1169
[4] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction
(Oxford University Press: Oxford)
[5] Angles d’Auriac J -Ch, Maillard J -M and Viallet C M 2002 J. Phys. A: Math. Gen. 35 9251 [6] Wu F Y and Wang Y K 1976 J. Math. Phys. 17 439 [7] Georges A, Hansel D, Le Doussal P and Maillard J -M 1987 J. Physique 48 1 [8] Meyer H, Angles d’Auriac J -Ch, Maillard J -M and Rollet G 1994 Physica A 208 223
[9] Boukraa S, Maillard J -M 2001 J. Stat. Phys. 102 641
[10] Nishimori H 2002 J. Phys. A: Math. Gen. 35 9541
[11] Griffiths R B 1972 in Phase Transitions and Critical Phenomena, Vol. 1, Eds C Domb and M S
Green, (Academic Press: London)
[12] Nishimori H 1986 J. Phys. Soc. Japan 55 3305
[13] Abarenkova N, Angles d’Auriac J-Ch, Boukraa S and Maillard J -M 1999 Physica D 130 27 [14] Abarenkova N, Angles d’Auriac J-Ch, Boukraa S, Hassani S and Maillard J -M 1999 Physica A
264 264
[15] GNU Multiprecision; see http://www.swox.com/gmp/.
[16] Nishimori H and Nemoto K 2002 J. Phys. Soc. Japan 71 1198
[17] Ozeki Y, Kasono K, Ito N and Miyashita S 2003 Physica A 321 271
[18] Ito N, and Ozeki Y 2003 Physica A 321 262
[19] AaraoReisFDA,deQueirozSLAanddosSantosRR1999Phys.Rev.B606740 [20] Singh R R P and Adler J 1996 Phys. Rev. B 54 364.
[21] Honecker A, Picco M and Pujol P 2001 Phys. Rev. Lett. 87 047201
[22] Merz F and Chalker J T 2002 Phys. Rev. B 65 054425
[23] Nishimori H 1979 J. Phys. C: Solid State Phys. 12 L905
[24] Nishimori H and Stephen M J 1983 Phys. Rev. B 27 5644
[25] Jacobsen J L and Picco M 2002 Phys. Rev. E 65 026113
[26] Wang C, Harrington J and Preskill J 2003 Ann. Phys., NY 303 31
[27] Angles d’ Auriac J-Ch, Maillard J-M and Wu F Y 1991 Physica A 177 114 [28] Angles d’ Auriac J-Ch, Maillard J-M and Wu F Y 1991 Physica A 179 496
[29] Domany E and Riedel E K 1978 Phys. Rev. Lett. 40 561
[30] Baxter R J, Perk J H H and Au-Yang H 1988 Phys. Lett. A 128 138

67

arXiv:cond-mat/0207694 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi
10.1088/0305-4470/35/39/303
Energy fluctuations at the multicritical point in two-dimensional spin glasses
Authors: Hidetoshi Nishimori, Cyril Falvo, Yukiyasu Ozeki
Submitted 24 September, 2002; v1 submitted 30 July, 2002; originally announced July 2002.
Comments: 9 pages, 7 figures; Note added
Journal ref: J. Phys. A 35 (2002) 8171
https://arxiv.org/abs/cond-mat/0207694

[1] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford: Oxford Univ. Press)
[2] Jacobsen J L and Picco M 2002 Phys. Rev. E 65 026113
[3] Nishimori H and Nemoto K 2002 J. Phys. Soc. Japan 71 1198
[4] Aara ̃oReisFDA,deQueirozSLAanddosSantosRR1999Phys.Rev.B606740 [5] Le Doussal P and Harris A B 1988 Phys. Rev. Lett. 61 625
[6] Nishimori H 1986 J. Phys. Soc. Japan 55 3305
[7] Merz F and Chalker J T 2002 Phys. Rev. B 65 054425

68

arXiv:cond-mat/0207310 [pdf, ps, other] cond-mat.dis-nn
doi 10.1016/S0378-4371(03)00023-2
Absence of the Effects of Vortices in the Gauge Glass
Authors: Toshiyuki Hamasaki, Hidetoshi Nishimori
Submitted 12 July, 2002; originally announced July 2002.
Comments: 12 pages, 2 figures; proceedings of StatPhys-Taiwan 2002
Journal ref: Physica A 321 (2003) 114-123
https://arxiv.org/abs/cond-mat/0207310

[1] M. Rubinstein, B. Shraiman and D. R. Nelson, Phys. Rev. B 27, 1800 (1983).
[2] E. Granato and J. M. Kosterlitz, Phys. Rev. B 33, 6553 (1986).
[3] W. Y. Shih, C. Ebner and D. Stroud, Phys. Rev. B 30, 134 (1984).
[4] T. Nattermann, S. Scheidl, S. E. Korshunov and M. S. Li, J. Phys. (France) 5, 565 (1995).
[5] S. Sheidl, Phys. Rev. B 55, 457 (1997).
[6] J. Maucourt and D. R. Grempel, Phys. Rev. B 56, 2572 (1997).
[7] D. Carpentier and P. Doussal, Nucl. Phys. B 588, 565 (1993).
[8] C. Mudry and X-G. Wen, Nucl. Phys. B 549, 613 (1999).
[9] H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981).
[10] Y. Ozeki and H. Nishimori, J. Phys. A 26, 3399 (1993).
[11] H. Nishimori, “Statistical Physics of Spin Glasses and Information Processing: An Introduction” Oxford University Press, (2001).
[12] J. Villain, J. Phys. C 10, 4793 (1977).
[13] L-H. Tang, Phys. Rev. B 54, 3350-3366 (1996).

69

arXiv:cond-mat/0206438 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi 10.1088/0305-4470/35/45/304
Derivatives and inequalities for order parameters in the Ising spin glass
Authors: Hidetoshi Nishimori
Submitted 1 October, 2002; v1 submitted 24 June, 2002; originally announced June 2002.
Comments: 10 pages; 3 figures; new inequalities added, title slightly changed
Journal ref: J. Phys. A 35 (2002) 9541.
https://arxiv.org/abs/cond-mat/0206438

[1] Young A P (Ed.) 1998 Spin Glasses and Random Fields (Singapore: World Scientific)
[2] Nishimori H 1981 Prog. Theor. Phys. 66 1169
[3] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction
(Oxford: Oxford University Press)
[4] Nishimori H and Sollich P 2000 J. Phys. Soc. Japan 69 Suppl. A 160
[5] Nishimori H 1993 J. Phys. Soc. Japan 62 2973
[6] Nishimori H and Sherrington D 2001 in Disordered and Complex Systems (Eds. Sollich P, Coolen
A C C, Hughston L P and Streater R F) p. 67 (Melville: AIP)
[7] Sherrington D and Kirkpatrick S 1975 Phys. Rev. Lett. 35 1792
[8] Ozeki Y and Nishimori H 1993 J. Phys. A: Math. Gen. 26 3399
[9] Nishimori H 1986 J. Phys. Soc. Japan 55 3305
[10] de Almeida J R L and Thouless D J 1978 J. Phys. A: Math. Gen. 11 983
[11] Le Doussal P and Harris A B 1989 Phys. Rev. B 40 9249
[12] Hukushima K 2000 J. Phys. Soc. Japan 69 631

70

arXiv:cond-mat/0201121 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi 10.1016/S0378-4371(02)01228-1
Complex and Non-Complex Phase Structures in Models of Spin Glasses and Information Processing
Authors: Hidetoshi Nishimori
Submitted 8 January, 2002; originally announced January 2002.
Comments: 13 pages; Proceedings of the International Symposium on Slow Dynamics in Nature, Seoul, Korea, November 2001; to be published in Physica A
Journal ref: Physica A 315 (2002) 243-254
https://arxiv.org/abs/cond-mat/0201121

[1] H. Nishimori, Statistical Physics of Spin Glasses and Information Processing : An Introduction, Oxford Univ. Press (Oxford, 2001).
[2] H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981).
[3] N. Sourlas, Nature 339, 693 (1989).
[4] Y. Ozeki and H. Nishimori, J. Phys. A 26, 3399 (1993).
[5] Y. Ozeki, J. Phys. A 28, 3645 (1995).
[6] Y. Ozeki, J. Phys. Cond. Matt. 9, 11171 (1997).
[7] H. Nishimori and D. Sherrington, In Disordered and Complex Systems, Eds. P. Sollich, A. C. C. Coolen, L. P. Hughston and R. F. Streater, AIP Conference Proceedings 553 (AIP, Melville, New York, 2001).
[8] D. C. Mattis, Phys. Lett. A 56, 421 (1976).
[9] P. Ruja ́n, Phys. Rev. Lett. 70, 2968 (1993).
[10] H. Nishimori, J. Phys. Soc. Jpn. 62, 2973 (1993).
[11] N. Sourlas, Europhys. Lett. 25, 159 (1994).
[12] Y. Iba, J. Phys. A 32, 3875 (1999).
[13] Y. Kabashima, T. Murayama and D. Saad, Phys. Rev. Lett. 84, 2030 (2000).

71

arXiv:cond-mat/0201056 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi 10.1016/S0378-4371(02)00486-7
Exact results on spin glass models
Authors: Hidetoshi Nishimori
Submitted 4 January, 2002; originally announced January 2002.
Comments: 9 pages, Proceedings of STATPHYS21, to be published in Physica A
Journal ref: Physica A 306, 68-75 (2002)
https://arxiv.org/abs/cond-mat/0201056

[1] H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981).
[2] H. Nishimori, Statistical Physics of Spin Glasses and Information Processing : An Introduction, Oxford Univ. Press (Oxford, 2001).
[3] H. Nishimori, J. Phys. Soc. Jpn. 62, 2973 (1993).
[4] H. Nishimori and D. Sherrington, In Disordered and Complex Systems, Eds. P. Sollich, A. C. C. Coolen, L. P. Hughston and R. F. Streater, AIP Conference Proceedings 553 (AIP, Melville, New York, 2001).
[5] Y. Ozeki and H. Nishimori, J. Phys. A 26, 3399 (1993).
[6] J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973).
[7] S. Scheidl, Phys. Rev. B 55, 457 (1997).
[8] L.-H. Tang, Phys. Rev. B 54, 3350 (1997).
[9] D. Carpentier and P. Le Doussal, Nucl. Phys. B 588 [FS], 565 (2000).

72

arXiv:cond-mat/0111354 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi
10.1143/JPSJ.71.1198
Duality and Multicritical Point of Two-Dimensional Spin Glasses
Authors: Hidetoshi Nishimori, Koji Nemoto
Submitted 4 February, 2002; v1 submitted 19 November, 2001; originally announced November 2001.
Comments: 4 pages, 1 figure; Reference updated, definition of \tilde{V} added; to be published in J. Phys. Soc. Jpn
Journal ref: J. Phys. Soc. Jpn. 71 (2002) 1198
https://arxiv.org/abs/cond-mat/0111354

F. D. A. Aarao Reis, S. L. A. de Queiroz and R. R. dos Santos: Phys. Rev. B 60 (1999) 6740.
R. R. P. Singh and J. Adler: Phys. Rev. B 54 (1996) 364.
Y. Ozeki and N. Ito: J. Phys. A 31 (1998) 5451.
A. Honecker, M. Picco and P. Pujol: Phys. Rev. Lett. 87 (2001) 047201.
F. Merz and J. T. Chalker: Phys. Rev. B 65 (2002) 054425.
J. L. Jacobsen and M. Picco: cond-mat/0105587.
S. Cho and M. P. A. Fisher: Phys. Rev. B 55 (1997) 1025.
I. A. Gruzberg, N. Read and A. W. W. Ludwig: Phys. Rev. B 63 (2001) 104422.
N. Read and A. W. W. Ludwig: Phys. Rev. B 63 (2000) 024404.
T. Senthil and M. P. A. Fisher: Phys. Rev. B 61 (2000) 9690.
E. S. Sørensen, M. J. P. Gingras and D. A. Huse: Europhys. Lett. 44 (1998) 504.
F. Y. Wu and Y. K. Wang: J. Math. Phys. 17 (1976) 439.
H. Nishimori: J. Phys. C 12 (1979) L905.
A. Aharony and M. J. Stephen: J. Phys. C 13 (1980) L407.
H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169.
H. Nishimori and M. J. Stephen: Phys. Rev. B 27 (1983) 5644.
A. George, D. Hansel, P. Le Doussal and J. M. Maillard: J. Physique 48 (1987) 1.
H. Nishimori: Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford Univ. Press, Oxford, 2001).
E. Domany: J. Phys. C 12 (1979) L119.

73

arXiv:cond-mat/0111003 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi 10.1209/epl/i2002-00576-1
Comment on 'Statistical mechanics of CDMA multiuser demodulation'
Authors: H. Nishimori
Submitted 31 October, 2001; originally announced November 2001.
Comments: To be published in Europhys. Lett
Journal ref: Europhys. Lett. 57 (2002) 302
https://arxiv.org/abs/cond-mat/0111003

[1] Tanaka T., Europhys. Lett., 54 (2001) 540.
[2] Nishimori H. and Sherrington D., Disordered and Complex Systems, edited by P. Sollich,
A. C. C. Coolen, L. P. Hughston, and R. F. Streater (AIP, Melville) 2001, p. 67.
[3] Nishimori H., Statistical Physics of Spin Glasses and Information Processing : An Introduction
(Oxford University Press, Oxford) 2001.

74

arXiv:cond-mat/0103292 [pdf, ps, other] cond-mat.dis-nn
doi 10.1088/0305-4470/34/14/303
Multispin Ising spin glasses with ferromagnetic interactions
Authors: Peter Gillin, Hidetoshi Nishimori, David Sherrington
Submitted 20 March, 2001; v1 submitted 14 March, 2001; originally announced March 2001.
Comments: 16 pages, AMS LaTeX, 14 EPS figures; one minor correction to (42)
https://arxiv.org/abs/cond-mat/0103292

[1] M. M ́ezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, 1987).
[2] D. Sherrington, “Spin Glasses”, in Physics of Novel Materials (World Scientific, 1999), edited by M. P. Das.
[3] J. A. Mydosh, Spin glasses: an experimental introduction (Taylor and Francis, 1993).
[4] J. A. Hertz, A. Krogh, and R. G. Palmer, Introduction to the theory of neural computation
(Addison–Wesley, 1991).
[5] P. G. Wolynes, J. N. Onuchic, and D. Thirumalai, Science 267, 1619 (1995).
[6] N. Sourlas, Nature 339, 693 (1989).
[7] E. Gardner, Nucl. Phys. B 257, 747 (1985).
[8] V. M. de Oliveira and J. F. Fontanari, J. Phys. A 32, 2285 (1998).
[9] H. Nishimori and K. Y. M. Wong, Phys. Rev. E 60, 132 (1999).
[10] P. Gillin and D. Sherrington, J. Phys. A 33, 3081 (2000).
[11] D. Sherrington and S. Kirkpatrick, Phys. Rev. B 17, 4384 (1978).
[12] G. Parisi, J. Phys. A 13, 1101 (1979).
[13] B. Derrida, Phys. Rev. B 24, 2613 (1981).
[14] T. C. Dorlas and J. R. Wedagedera, Phys. Rev. Lett. 83, 4441 (1999).
[15] J. R. L. de Almeida and D. J. Thouless, J. Phys. A 11, 983 (1978).
[16] G. Parisi, J. Phys. A 13, L115 (1979).
[17] H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981).
[18] P. Gillin and D. Sherrington, to appear in J. Phys. A (2001), cond-mat/0101245.

75

arXiv:cond-mat/0008139 [pdf, ps, other] cond-mat.dis-nn
doi 10.1063/1.1358165
Absence of Replica Symmetry Breaking in a Region of the Phase Diagram of the Ising Spin Glass
Authors: Hidetoshi Nishimori, David Sherrington
Submitted 8 August, 2000; originally announced August 2000.
Comments: 6 pages, 3 figures, uses aipproc.sty
Journal ref: in "Disordered and Complex Systems", Ed. P. Sollich et al, AIP Conf. Proc. 553, p. 67 (2001)
https://arxiv.org/abs/cond-mat/0008139

Nishimori H., Prog. Theor. Phys. 69, 1169 (1981).
Nishimori H., Spin Glass Theory and Statistical Mechanics of Information, Iwanami: Tokyo, 1999 (in Japanese).
Gillin P., Sherrington D., and Nishimori H., (in preparation).
M ́ezard M., Parisi G., and Virasoro M. A., Spin Glass Theory and Beyond, Singapore: World Scientific, 1987.

76

arXiv:cond-mat/0005125 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi 10.1143/JPSJ.69.3200
Exact Solution of the Infinite-Range Quantum Mattis Model
Authors: P. Sollich, Hidetoshi Nishimori, A. C. C. Coolen, A. J. van der Sijs
Submitted 7 May, 2000; originally announced May 2000.
Comments: 14 pages, 11 figures
Journal ref: J. Phys. Soc. Jpn. 69 (2000) 3200
https://arxiv.org/abs/cond-mat/0005125

R. N. Bhatt: in Spin Glasses and Random Fields, Ed. A. P. Young, (World Scientific, Singapore, 1998), p. 225.
H. Nishimori and Y. Nonomura: J. Phys. Soc. Jpn. 65 (1996) 3780.
D. C. Mattis: Phys. Lett. A 56 (1976) 421.
D. Sherrington: J. Phys. C 10 (1977) L7.
H. Nishimori: J. Stat. Phys. 26 (1981) 839.
A. Aharony: Phys. Rev. B 18 (1978) 3318.
J. W. Gibbs: The Collected Works of J. Willard Gibbs; The Scientific Papers of J. Willard Gibbs, reprinted (Dover, New York, 1960).
G. R. Brannock, J. Chem. Phys. 95 (1991) 612.

77

arXiv:cond-mat/0003098 [pdf, ps, other] cond-mat.dis-nn cond-mat.stat-mech
doi 10.1103/PhysRevE.62.179
Error-correcting codes and image restoration with multiple stages of dynamics
Authors: K. Y. Michael Wong, Hidetoshi Nishimori
Submitted 7 March, 2000; originally announced March 2000.
Comments: 30 pages, 11 figures
https://arxiv.org/abs/cond-mat/0003098

[1] R. J. Eliece, The Theory of Information and Coding, Encyclopedia of Mathematics and its Applications (Addison-Wesley, Reading, MA 1977).
[2] N. Sourlas, Nature 339, 693 (1989).
[3] Y. Kabashima and D. Saad, Europhys. Lett. 45, 97 (1999).
[4] S. Geman and D. Geman, IEEE Trans. PAMI 6, 721 (1984).
[5] H. Nishimori and K. Y. M. Wong, Phys. Rev. E 60, 132 (1999).
[6] H. Nishimori, J. Phys. Soc. Jpn. 62, 2973 (1993).
[7] Z. Zhou, R. M. Leathy, and J. Qi, IEEE Trans. Image Proc. 6, 844 (1997).
[8] D. J. C. Mackay, Neural Computation 4, 415 (1992).
[9] J. M. Pryce and A. D. Bruce, J. Phys. A 28, 511 (1995).
[10] K. Y. M. Wong, Europhys. Lett. 36, 631 (1996).
[11] M. M ́ezard, G. Parisi, and V.A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore 1987).
[12] K. Y. M. Wong, Europhys. Lett. 30, 245 (1995).
[13] K. Y. M. Wong, Advances in Neural Information Processing Systems 9, 302 (1997).
[14] B. J. Frey, Graphical Models for Machine Learning and Digital Communication (MIT Press, 1998).
[15] Y. Kabashima and D. Saad, Europhys. Lett. 44, 668 (1998).
[16] C. Berrou, A. Glavieux, and P. Thitimajshima, Proc. IEEE Int. Conf. Comm. ’93, 1064 (1993).

78

arXiv:cond-mat/9902312 [pdf, ps, other] cond-mat.dis-nn
doi 10.1103/PhysRevE.60.132
Statistical mechanics of image restoration and error-correcting codes
Authors: H. Nishimori, K. Y. M. Wong
Submitted 23 February, 1999; originally announced February 1999.
Comments: 20 pages, 9 figures, ReVTeX
https://arxiv.org/abs/cond-mat/9902312

[1] R. J. Eliece, The Theory of Information and Coding, Encyclopedia of Mathematics and its Applications (Addison-Wesley, Reading, MA, 1977).
[2] J. M. Pryce and A. D. Bruce, J. Phys. A 28, 511 (1995).
[3] N. Sourlas, Nature 339, 693 (1989).
[4] D. C. Mattis, Phys. Lett. A 56, 421 (1976).
[5] J. C. A. van der Lubbe, Information Theory (Cambridge, New York, 1997).
[6] P. Ruja ́n, Phys. Rev. Lett. 70, 2968 (1993).
[7] H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981).
[8] H. Nishimori, J. Phys. Soc. Jpn. 62, 2973 (1993).
[9] N. Sourlas, Europhys. Lett. 25, 159 (1994).
[10] Y. Kabashima and D. Saad, Europhys. Lett. 45, 97 (1999).
[11] S. Geman and D. Geman, IEEE Trans. PAMI 6, 721 (1984).
[12] J. Zerubia and R. Chellapa, IEEE Trans. Neural Net. 4, 703 (1993).
[13] K. Tanaka and T. Morita, Phys. Lett. A 203, 122 (1995); Physica A 223, 244 (1996);
T. Morita and K. Tanaka, Pattern Recog. Lett. 18, 1479 (1998).
[14] J. L. Marroquin, S. Mitter and T. Poggio, J. Am. Stat. Assoc. 82, 76 (1987).
[15] Z. Zhou, R. M. Leathy and J. Qi, IEEE Trans. Image Proc. 6, 844 (1997).
[16] K. H. Fischer and J. A. Hertz, Spin glasses (Cambridge, New York, 1991).
[17] Rigorously speaking, the state of Fig. 6 (a) is a metastable state, not in full thermal
equilibrium in which most of the pixels are either black or white when Ts is below the critical point. We nevertheless show the example (a) in Fig. 6 because it represents true equilibrium situations rather faithfully (if we look only at the mostly white domain, for example) and simultaneously it is easier to intuitively recognize the differences among (a)-(e) than by using mostly black or white images. The simulations of Figs. 4 and 5 were carried out in true equilibrium.
[18] E. Gardner, Nucl. Phys. B257 [FS14], 747 (1985).
[19] D.J. Gross and M. M ́ezard, Nucl. Phys. B240 [FS12], 431 (1984).
[20] K. Y. M. Wong, Europhys. Lett. 36, 631 (1996).
[21] K. Y. M. Wong and H. Nishimori, (unpublished).
[22] B. Bergersen and M. Plischke, Equilibrium Statistical Mechanics, 2nd edition (World
Scientific, Singapore, 1994).

79

arXiv:cond-mat/9804280 [pdf, ps, other] cond-mat.stat-mech cond-mat.dis-nn
doi
10.1103/PhysRevE.58.5355
Quantum Annealing in the Transverse Ising Model
Authors: Tadashi Kadowaki, Hidetoshi Nishimori
Submitted 25 April, 1998; originally announced April 1998.
Comments: 15 pages, RevTeX, 8 figures
Report number: TITCMT-98-4
Journal ref: Phys. Rev. E 58, 5355 (1998)
https://arxiv.org/abs/cond-mat/9804280

[1] S. Kirkpatrick, C. D. Gelett and M. P. Vecchi, Science 220, 671 (1983).
[2] S. Geman and D. Geman, IEEE Trans. PAMI 6, 721 (1984).
[3] C. Tsallis and D. A. Stariolo, Physica A 233, 395 (1996).
[4] H. Nishimori and J. Inoue (submitted to J. Phys. A).
[5] H. Nishimori and Y. Nonomura, J. Phys. Soc. Jpn. 65, 3780 (1996).
[6] B. K. Chakrabrati, A. Dutta and P. Sen, Quantum Ising Phases and Transitions in Transverse Ising Models (Springer, Berlin, 1996).
[7] T. Sato, N. Hatano, M. Suzuki and H. Takayama (unpublished).
[8] D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).
[9] S. Miyashita, Prog. Theor. Phys. 69, 714 (1983).
[10] C. Zener, Proc. R. Soc. London, Ser A 137, 696 (1932).
[11] S. Miyashita, J. Phys. Soc. Jpn. 64, 3207 (1995).
[12] S. Miyashita, J. Phys. Soc. Jpn. 65, 2734 (1996).
[13] H. De Raedt, S. Miyashita, K. Saito, D. Grac ́ıa-Pablos and N. Grac ́ıa, Phys. Rev. B 56,
11761 (1997).
[14] A. Erd ́elyi et al., Higher Transcendental Functions (MaGraw-Hill, New York, 1953).

80

arXiv:cond-mat/9801206 [pdf, ps, other] cond-mat.stat-mech
doi
10.1088/0305-4470/31/26/007
Convergence of simulated annealing by the generalized transition probability
Authors: Hidetoshi Nishimori, Jun-ichi Inoue
Submitted 21 January, 1998; originally announced January 1998.
Comments: 11 pages
Report number: TITSTAT-98-NIS1
https://arxiv.org/abs/cond-mat/9801206

[1] S. Kirkpartick, C. D. Gelett and M. P. Vecchi, Science 220, 671 (1983).
[2] Y. Uesaka, Mathematical Foundations of Neurocomputing (Kindai Kagakusha, Tokyo, 1993) (in Japanese), Chap. 4.
[3] E. H. L. Aarts and J. Korst, Simulated Annealing and Boltzmann Machines: a Stochastic Approach to Combinatorial Optimization and Neural Computing (Wiley, 1989), Chap. 3.
[4] S. Geman and D. Geman, IEEE Trans. PAMI 6, 721 (1984).
[5] H. Szu and R. Hartley, Phys. Lett. 122A, 157 (1987).
[6] C. Tsallis and D. A. Stariolo, Physica A 233, 395 (1996).
[7] T. J. P. Penna, Phys. Rev. E51, R1 (1995).
[8] I. Andricioaei and J. E. Straub, Phys. Rev. E53, R3055 (1996).
[9] S. Shinomoto and Y. Kabashima, J. Phys. A 24, L141 (1991).

81

arXiv:cond-mat/9708096 [pdf, ps, other] cond-mat.dis-nn
A Simple Perceptron that Learns Non-Monotonic Rules
Authors: Jun-ichi Inoue, Hidetoshi Nishimori, Yoshiyuki Kabashima
Submitted 13 August, 1997; originally announced August 1997.
Comments: LaTeX 10 pages including 6 ps figures, using llncs.sty, Proc. of Theoretical Aspects of Neural Computation 97, to be published from Springer-Verlag
https://arxiv.org/abs/cond-mat/9708096

J. A. Hertz, A. Krogh and R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Redwood City, 1991).
T. H. Watkin, A. Rau and M. Biehl, Rev. Mod. Phys. 65, 499 (1993).
M. Opper and W. Kinzel, in Physics of Neural Networks III, Eds. E. Domany, K.
L. van Hemmen and K. Schulten (Springer, Berlin, 1995).
S. Amari, IEEE Trans. EC-16, 299 (1967).
S. Amari, Neural Networks, 6, 161 (1993).
S. Amari and N. Murata, Neural. Comp. 1, 140 (1993).
S. B ̈os, W. Kinzel and M. Opper, Phys. Rev. E 47, 1384 (1993).
Y. Kabashima, J. Phys. A: Math. Gen. 27, 1917 (1994).
M. Bouten, J. Schietse and C. Van den Broeck, Phys. Rev. E 52, 1958 (1995).
C. Van den Broeck and P. Reimann, Phys. Rev. Lett. 76, 2188 (1996).
T. H. Watkin and A. Rau, Phys. Rev. A 45, 4111 (1992).
Y. Kabashima and S. Shinomoto, Neural Comp. 7, 158 (1995).
J. W. Kim and H. Sompolinsky, Phys. Rev. Lett. 76 3021 (1996).
D. Saad and S. A. Solla, Phys. Rev. E 52 4255 (1995).
Y. Kabashima and J. Inoue, (in preparation).
J. Inoue, H. Nishimori and Y. Kabashima, J. Phys. A: Math. Gen. 30, 3795 (1997)
J. Inoue and H. Nishimori, Phys. Rev. E 55, 4544 (1997).
G. Gyo ̈rgyi and N. Tishby, Neural Networks and Spin Glasses (Singapore: World
Scientific, 1990).
M. Opper and D. Haussler, Phys. Rev. Lett. 66, 2677 (1991).
M. Biehl and P. Rieglar, Europhys. Lett. 27, 85 (1994).
W. Kinzel and P. Ruj ́an Europhys. Lett. 23, 473 (1990).
O. Kinouchi and N. Caticha, J. Phys. A: Math. Gen. 26, 6161 (1993).

82

arXiv:cond-mat/9705190 [pdf, ps, other] cond-mat.dis-nn
doi
10.1103/PhysRevE.58.849
Generalization ability of a perceptron with non-monotonic transfer function
Authors: Jun-ichi Inoue, Hidetoshi Nishimori, Yoshiyuki Kabashima
Submitted 28 January, 1998; v1 submitted 19 May, 1997; originally announced May 1997.
Comments: Latex 20 pages with 10 figures
https://arxiv.org/abs/cond-mat/9705190

[1] S. Amari, IEEE Trans. EC-16 299 (1967).
[2] J. A. Hertz, A. Krogh and R. G. Palmer, Introduction to the Theory of Neural Compu-
tation, Redwood City: Addison-Wesley (1991).
[3] T. H. L. Watkin, A. Rau and M. Biehl, Rev. Mod. Phys. 65 499 (1993).
[4] M. Opper and W. Kinzel, in Physics of Neural Networks III, Eds. E. Domany, J. L. van Hemmen and K. Schulten, Berlin: Springer (1995).
[5] M. Griniasti and H. Gutfreund, J. Phys. A: Math. Gen. 24, 715 (1991).
[6] R. Meir and J. F. Fontanari, Phys. Rev. A 45, 8874 (1992).
[7] O. Kinouchi and N. Caticha, Phys. Rev. E 54, R54 (1996).
[8] Y. Kabashima, J. Phys. A: Math. Gen. 27, 1917 (1994).
[9] H. Sompolinsky, N. Barkai and H. S. Seung, Neural Networks: The Statistical Mechanics Perspective, Eds. J. H. Oh, C. Kwon and S. Cho, World Scientific (1995).
[10] D. Saad and S. A. Solla, Phys. Rev. E 52 4225 (1995).
[11] M. Morita, S. Yoshizawa and K. Nakano, Trans. Inst. Electron. Inf. Commun. J73-D-II, 242 (1993) (in Japanese)
[12] H. Nishimori and I. Opris, Neural Networks 6, 1061 (1993).
[13] J. Inoue, J. Phys. A: Math. Gen. 29, 4815 (1996).
[14] M. Morita, Neural Networks 9, 1477 (1996).
[15] G. Boffetta, R. Monasson and R. Zecchina, J. Phys. A: Math. Gen. 26, L507 (1993).
[16] R. Monasson and D. O’Kane, Europhys. Lett. 27, 85 (1994).
[17] A. Engel and L. Reimers, Europhys. Lett 28, 531 (1994).
[18] M. Biehl and P. Riegler, Europhys. Lett. 28, 525 (1994).
[19] J. Inoue and H. Nishimori, Phys. Rev. E 55 4544 (1997).
[20] J. Inoue, H. Nishimori and Y. Kabashima, J. Phys. A: Math. Gen. 30 3795 (1997).
[21] C. Van den Broeck, Proc. of Theoretical Aspects of Neural Computation 97 (TANC-97),
to be published, Springer-Verlag.
[22] C. Van den Broeck and P. Reimann, Phys. Rev. Lett. 76, 2188 (1996).
[23] O. Kinouchi and N. Caticha, J. Phys. A: Math. Gen. 26, 6243 (1992).
[24] R. Simonetti and N. Caticha, J. Phys. A: Math. Gen. 29, 4859 (1996).
[25] W. Kinzel and P. Ruja ́n, Europhys. Lett. 13, 473 (1990).

83

arXiv:cond-mat/9705019 [pdf, ps, other] cond-mat.dis-nn
doi
10.1143/JPSJ.66.1962
High-Temperature Dynamics of Spin Glasses
Authors: Michiko Yamana, Hidetoshi Nishimori, Tadashi Kadowaki, D. Sherrington
Submitted 2 May, 1997; originally announced May 1997.
Comments: 24 pages, figures available on request, LaTeX, uses jpsj.sty, to be published in J. Phys. Soc. Jpn. 66 No. 7 (1997)
https://arxiv.org/abs/cond-mat/9705019

[1] D. Sherrington and S. Kirkpatrick: Phys. Rev. Lett. 35 (1975) 1792.
[2] L. F. Cugliandolo and J. Kurchan: Phys. Rev. Lett. 71 (1993) 173.
[3] A.C.C. Coolen, S.N. Laughton and D. Sherrington: Phys. Rev. B 53 (1996) 8184.
[4] S.N. Laughton, A.C.C. Coolen and D. Sherrington: J. Phys. A: Math. Gen. 29 (1996) 763.
[5] H. Nishimori and M. Yamana: J. Phys. Soc. Jpn. 65 (1996) 3.
[6] H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169.
[7] Y. Ozeki and H. Nishimori: J. Phys. Soc. Jpn. 56 (1987) 3265.
[8] M. Randeria, J. P. Sethna and R. G. Palmer: Phys. Rev. Lett. 54 (1985) 1321.
[9] M. Thomsen, M.F. Thorpe, T.C. Choy, D. Sherrington and H.-J. Sommers: Phys. Rev. B 33 (1986) 3.

84

arXiv:cond-mat/9703020 [pdf, ps, other] cond-mat nlin.AO
doi 10.1088/0305-4470/30/11/012
On-line learning of non-monotonic rules by simple perceptron
Authors: Jun-ichi Inoue, Hidetoshi Nishimori, Yoshiyuki Kabashima
Submitted 2 March, 1997; originally announced March 1997.
Comments: LaTeX 20 pages using IOP LaTeX preprint style file, 14 figures
https://arxiv.org/abs/cond-mat/9703020

[1] Hertz J A, Krogh A and Palmer R G 1991 Introduction to the Theory of Neural Computation, (Redwood City: Addison-Wesley)
[2] Watkin T H L, Rau A and Biehl M 1993 Rev. Mod. Phys. 65 499
[3] Opper M and Kinzel M 1995 in Physics of Neural Networks III, Eds. Domany E, van Hemmen J
L and Schulten K (Berlin: Springer)
[4] Kim J W and Sompolinsky H 1996 Phys. Rev. Lett. 76 3021
[5] Saad D and Solla S A 1995 Phys. Rev. E 52 4225
[6] Watkin T L H and Rau A 1992 Phys. Rev. A 45 4111
[7] Morita M, Yoshizawa S and Nakano K 1990 Trans. IEICE J73-D-II 242 [8] Nishimori H and Opris I 1993 Neural Networks 6 1061
[9] Inoue J 1996 J. Phys. A: Math. Gen. 29 4815
[10] Boffetta G, Monasson R and Zecchina R 1993 J. Phys. A: Math. Gen. 26 L507 [11] Monasson R and O’Kane D 1994 Europhys. Lett. 27 85
[12] Kabashima Y 1994 J. Phys. A: Math. Gen. 27 1917
[13] Biehl M and Schwarze H 1992 Europhys. Lett. 20 733
[14] Vallet F 1989 Europhys. Lett. 9 315
[15] Barkai N, Seung H S and Sompolinsky H 1995 Proc.of Advances in Neural Information Processing System (NIPS) 7 303
[16] Biehl M, Riegler P and Stechert M 1995 Phys. Rev. E 52 4624
[17] Kinouchi O and Caticha N 1992 J. Phys. A: Math. Gen. 26 6243
[18] Opper M, Kinzel W, Kleinz J and Nehl R 1990 J. Phys. A: Math. Gen. 23 L581 [19] Kabashima Y and Shinomoto S 1995 Neural Comp. 7 158
[20] Kinzel W and Ruja ́n P 1990 Europhys. Lett. 13 473

85

arXiv:cond-mat/9703019 [pdf, ps, other] cond-mat nlin.AO
doi
10.1103/PhysRevE.55.4544
On-Line AdaTron Learning of Unlearnable Rules
Authors: Jun-ichi Inoue, Hidetoshi Nishimori
Submitted 2 March, 1997; originally announced March 1997.
Comments: RevTeX 17 pages, 8 figures, to appear in Phys.Rev.E
https://arxiv.org/abs/cond-mat/9703019

[1] J. A. Hertz, A. Krogh and R. G. Palmer, Introduction to the Theory of Neural Compu-
tation (Addison-Wesley, Redwood City, 1991).
[2] T. H. Watkin, A. Rau and M. Biehl, Rev. Mod. Phys. 65,499 (1993).
[3] M. Opper and W. Kinzel, in Physics of Neural Networks III, Eds. E. Domany, J. L. van Hemmen and K. Schulten (Springer, Berlin, 1995).
[4] T. H. Watkin and A. Rau, Phys. Rev. A 45, 4111 (1992).
[5] M. Morita, S. Yoshizawa and K. Nakano, Trans. IEICE J73-D-II, 242 (1990) (in
Japanese).
[6] H. Nishimori and I. Opris, Neural Networks 6, 1061 (1993).
[7] J. Inoue, J. Phys. A: Math. Gen. 29, 4815 (1996).
[8] G. Boffetta, R. Monasson and R. Zecchina, J. Phys. A: Math. Gen. 26, L507 (1993).
[9] R. Monasson and D. O’Kane, Europhys. Lett. 27, 85 (1994).
[10] J. Inoue, H. Nishimori and Y. Kabashima, (unpublished).
[11] M. Biehl and P. Riegler, Europhys. Lett. 28, 525 (1994).
[12] J. K. Anlauf and M. Biehl, Europhys. Lett. 10, 687 (1989).
[13] P. Riegler, M. Biehl, S. A. Solla and C. Marangi, in Proc. of Italian Workshop on Neural Nets VII (1995).
[14] M. Opper, W. Kinzel, J. Kleinz and R. Nehl, J. Phys. A: Math. Gen. 23, L581(1990).
[15] O. Kinouchi and N. Caticha, J. Phys. A: Math. Gen. 26, 6161 (1993).
[16] Y. Kabashima and S. Shinomoto, Neural Comp. 7, 158 (1995).

86

arXiv:cond-mat/9603105 [pdf, ps, other] cond-mat
doi
10.1143/JPSJ.65.3780
Quantum Effects in Neural Networks
Authors: Hidetoshi Nishimori, Yoshihiko Nonomura
Submitted 14 March, 1996; originally announced March 1996.
Comments: 34 pages, LaTeX, 9 PS figures, uses jpsj.sty
https://arxiv.org/abs/cond-mat/9603105

[1] D.J. Amit, H. Gutfreunt and H. Sompolinsky: Phys. Rev. A 32 (1985) 1007.
[2] D.J. Amit, H. Gutfreunt and H. Sompolinsky: Ann. Phys. 173 (1987) 30.
[3] D. Sherrington and S. Kirkpatrick: Phys. Rev. Lett. 35 (1975) 1792.
[4] D.J. Amit: Modeling Brain Functioning (Cambridge Univ. Press, Cambridge, 1989), section 2.1.3.
[5] H.P. Stapp: Found. Phys. 21 (1991) 1451.
[6] F. Beck and J.C. Eccles: Proc. Natl. Acad. Sci. USA 89 (1992) 11357.
[7] R. Penrose: The Emperor’s New Mind (Oxford Univ. Press, Oxford, 1989); R. Penrose: Shadows of the Mind
(Oxford Univ. Press, Oxford, 1994)
[8] Y. Nonomura and H. Nishimori: preprint.
[9] M. Suzuki: Prog. Theor. Phys. 56 (1976) 1454.
[10] K.D. Usadel and B. Schmitz: Solid St. Commun. 64 (1987) 975.
[11] H. Ishii and T. Yamamoto: J. Phys. C 18 (1985) 6255; Ya.V. Fedorov and E.F. Shender: JETP Lett. 43 (1986)
682.
[12] J. Hertz, A. Krogh and R.G. Palmer: Introduction to the Theory of Neural Computation (Addison-Wesley,
Redwood City, 1991)
[13] H. Steffan and R. Ku ̈hn: Z. Phys. B 95 (1994) 249.
[14] J.R.L. de Almeida and D.J. Thouless: J. Phys. A 11 (1978) 983.
[15] T. Gestzi: Physical Models of Neural Networks, Section 4.3 (World Scientific, Singapore, 1990).
[16] K. Binder and A.P. Young: Rev. Mod. Phys. 58 (1986) 801.

87

arXiv:cond-mat/9601033 [pdf, ps, other] cond-mat
doi
10.1143/JPSJ.65.1609
Exact Ground-State Energy of the Ising Spin Glass on Strips
Authors: Tadashi Kadowaki, Yoshihiko Nonomura, Hidetoshi Nishimori
Submitted 16 January, 1996; v1 submitted 10 January, 1996; originally announced January 1996.
Comments: 10 pages, 12 Postscript figures, LaTeX, uses subeqn.sty, minor changes in tex-file
Report number: TITCMT-95-30
Journal ref: J. Phys. Soc. Jpn. 66 (1996) 1609
https://arxiv.org/abs/cond-mat/9601033

[1] B. Derrida, J. Vannimenus and Y. Pomeau: J. Phys. C 11 (1978) 4749. [2] T. Morita and T. Horiguchi: J. Phys. C 13 (1980) 6483.
[3] B. Fechner and M. B laszyk: J. Phys. C 19 (1986) 2785.
[4] C. Dress, E. Amic and J. M. Luck: J. Phys. A 28 (1995) 135.
[5] T. D. Lee and C. N. Yang: Phys. Rev. 87 (1952) 410.
[6] Y. Ozeki and Y. Nonomura: J. Phys. Soc. Jpn. 64 (1995) 3128 [7] Y. Ozeki and H. Nishimori: J. Phys. Soc. Jpn. 56 (1987) 1568.

88

arXiv:cond-mat/9512167 [pdf, ps, other] cond-mat
doi
10.1143/JPSJ.65.3
Dynamical Probability Distribution Function of the SK Model at High Temperatures
Authors: Hidetoshi Nishimori, Michiko Yamana
Submitted 25 December, 1995; v1 submitted 25 December, 1995; originally announced December 1995.
Comments: LaTeX, 6 pages, Figures upon request (here revised), To be published in J. Phys. Soc. Jpn. 65 (1996) No.1
Report number: TITCMT-95-27
Journal ref: J. Phys. Soc. Jpn. 65 (1996) 3
https://arxiv.org/abs/cond-mat/9512167

[1] D. Sherrington and S. Kirkpatrick: Phys. Rev. Lett. 35(1975) 1792.
[2] K. Binder and A.P. Young: Rev. Mod. Phys. 58 (1986) 801.
[3] J.J. Hopfield: Proc. Natl. Acad. Sci. USA. 79 (1982) 2554.
[4] A.C.C. Coolen and Th.W. Ruijgrok: Phys. Rev. A 38 (1988) 4253.
[5] M. Shiino, H. Nishimori and M. Ono: J. Phys. Soc. Jpn. 58 (1989) 763. [6] U. Riedel, R. Ku ̈hn and J.L. van Hemmen: Phys. Rev. A 38 (1988) 1105. [7] A.C.C. Coolen and D. Sherrington: Phys. Rev. Lett. 71 (1993) 3886.
[8] A.C.C. Coolen and D. Sherrington: Phys. Rev. E. 49 (1994) 1921.
[9] T. Ozeki and H. Nishimori: J. Phys. A 27 (1994) 7061.
[10] A.C.C. Coolen and D. Sherrington: J. Phys. A 27 (1994) 7687.
[11] A.C.C. Coolen, S.N. Laughton and D. Sherrington: preprint (cond-mat/9507101). [12] S.N. Laughton, A.C.C. Coolen and D. Sherrington: preprint (cond-mat/9507108).

89

arXiv:cond-mat/9512142 [pdf, ps, other] cond-mat
Quantum Hopfield Model
Authors: Yoshihiko Nonomura, Hidetoshi Nishimori
Submitted 7 March, 1996; v1 submitted 21 December, 1995; originally announced December 1995.
Comments: 11 pages, 1 compressed/uuencoded postscript figure, revtex
Report number: TITCMT-95-28
https://arxiv.org/abs/cond-mat/9512142

[1] J. Hertz, A. Krogh and R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, Massachusetts, 1991).
[2] D. J. Amit, Modeling Brain Functioning (Cambridge University Press, Cambridge, 1988).
[3] H. P. Stapp: Found. Phys. 21, 1451 (1991).
[4] F. Beck and J. C. Eccles, Proc. Natl. Acad. Sci. USA 89, 11357 (1992).
[5] One may argue in this regard that the Hopfield model without the transverse-field term is already inadequate as a realistic model of the brain. The Hopfield model has nevertheless been the target of active research.
[6] J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
[7] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976).
[8] M. Suzuki, J. Math. Phys. 26, 601 (1985).
[9] D. J. Amit, H. Gutfreund and H. Sompolinsky, Ann. Phys. 173, 30 (1987).
REFERENCES
[10] H. Nishimori and Y. Nonomura (unpublished)
[11] T. Yamamoto and H. Ishii, J. Phys. C 20, 6053 (1987); K. D. Usadel and B. Schmitz, Solid State Commun. 64, 975 (1987); G. Bu ̈ttner and K. D. Usadel, Phys. Rev. B 42, 6385 (1990).
[12] D. C. Mattis, Phys. Lett. 56A, 421 (1976), 60A, 492 (1977) (erratum).
[13] T. Geszti, Physical Models of Neural Networks (World Scientific, Singapore, 1990).
[14] H. Steffan and R. Ku ̈hn, Z. Phys. B 95, 249 (1994).

コピペ誤り

１）番号が飛ぶ
一部の番号だけ順番が飛ぶ。改ページ、段落が関係することあり。
ページごと、段落ごとにコピペすれば大丈夫なこともある。

２）番号だけ連続で張り付き、論文と対応していない。
一部だけなる理由等は不明。

３）文字化け、文字抜け
アクセント記号が別になる。
フォントの種類が原因かどうか未調査。

４）改行が抜け、連続データになる

５）頁番号、標題が間に入る。

参考資料(reference)

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https://qiita.com/kaizen_nagoya/items/7e7eb7c543e0c18438c4

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自動制御、制御工学一覧（０）
https://qiita.com/kaizen_nagoya/items/7767a4e19a6ae1479e6b

Rust(0) 一覧　
https://qiita.com/kaizen_nagoya/items/5e8bb080ba6ca0281927

小川清最終講義、小川清最終講義（再）計画, Ethernet(100) 英語(100) 安全(100)
https://qiita.com/kaizen_nagoya/items/e2df642e3951e35e6a53

＜この記事は個人の過去の経験に基づく個人の感想です。現在所属する組織、業務とは関係がありません。＞
This article is an individual impression based on the individual's experience. It has nothing to do with the organization or business to which I currently belong.

文書履歴(document history)

ver. 0.01 初稿 20220101

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