量子コンピュータスクール
2005年3月22日 - 2005年3月24日
<この項は書きかけです。順次追記します。>
This article is not completed. I will add some words in order.
慶應義塾大学理工学部矢上キャンパス
伊藤公平、阿部英介、山口文子(慶應大学)、古田彩(日経サイエンス)
日本学術振興会、新機能素子研究開発協会
量子コンピュータ授業 #1 量子ビットと量子ゲート 阿部英介
https://www.youtube.com/watch?v=R2fyLl7KZXM&list=PLB1324F2305C028F7&index=1
![量子コンピュータ授業 #1 量子ビットと量子ゲート 阿部英介]
(http://img.youtube.com/vi/R2fyLl7KZXM/0.jpg)
g: grand
e: excited
computational basis
bracket
postulate 公理
unitary evolution
量子コンピュータ授業 #2 量子テレポーテーション 阿部英介
https://www.youtube.com/watch?v=mose-W49uF8&list=PLB1324F2305C028F7&index=2
量子コンピュータ授業 #3 ドイチェ・ジョザアルゴリズム 阿部英介
https://www.youtube.com/watch?v=vHIag48qFMA&list=PLB1324F2305C028F7&index=3
量子コンピュータ授業 #4 グローバーのアルゴリズム 阿部英介
https://www.youtube.com/watch?v=U6HszEyIuEw&list=PLB1324F2305C028F7&index=4
量子コンピュータ授業 #5 量子回路 阿部英介
https://www.youtube.com/watch?v=dIgllLXSMsg&list=PLB1324F2305C028F7&index=5
量子コンピュータ授業 #6 量子フーリエ変換 阿部英介
https://www.youtube.com/watch?v=weH43bUaPQg&list=PLB1324F2305C028F7&index=6
量子コンピュータ授業 #7 ショアの素因数分解アルゴリズム 阿部英介
https://www.youtube.com/watch?v=YBo36vtLObM&list=PLB1324F2305C028F7&index=7
量子コンピュータ授業 #8 量子コンピュータの歴史 古田彩
https://www.youtube.com/watch?v=wBilQWKd1yU&list=PLB1324F2305C028F7&index=8
![量子コンピュータ授業 #1 量子ビットと量子ゲート 阿部英介]
(http://img.youtube.com/vi/R2fyLl7KZXM/0.jpg)
量子コンピュータ授業 #9 量子力学基礎 山口文子
https://www.youtube.com/watch?v=8dT9M_irv44&list=PLB1324F2305C028F7&index=9
![量子コンピュータ授業 #9 量子力学基礎 山口文子]
(http://img.youtube.com/vi/8dT9M_irv44/0.jpg)
量子コンピュータ授業 #10 量子誤り訂正 山口文子
https://www.youtube.com/watch?v=M0Xf8lqfCic&list=PLB1324F2305C028F7&index=10
![量子コンピュータ授業 #10 量子誤り訂正 山口文子]
(http://img.youtube.com/vi/M0Xf8lqfCic/0.jpg)
量子コンピュータ授業 #11 古典線形符号 山口文子
https://www.youtube.com/watch?v=rvdAfpWmVC0&list=PLB1324F2305C028F7&index=11
![量子コンピュータ授業 #11 古典線形符号 山口文子]
(http://img.youtube.com/vi/rvdAfpWmVC0/0.jpg)
量子コンピュータ授業 #12 安定化符号 山口文子
https://www.youtube.com/watch?v=shssHavw1WM&list=PLB1324F2305C028F7&index=12
![量子コンピュータ授業 #12 安定化符号 山口文子]
(http://img.youtube.com/vi/shssHavw1WM/0.jpg)
量子コンピュータ授業 #13 対故障量子計算 山口文子
https://www.youtube.com/watch?v=7qWXVVtZazU&list=PLB1324F2305C028F7&index=13
![量子コンピュータ授業 #13 対故障量子計算 山口文子]
(http://img.youtube.com/vi/7qWXVVtZazU/0.jpg)
量子コンピュータ授業 #14 幾何学符号 山口文子
https://www.youtube.com/watch?v=NplMhUq4G8g&list=PLB1324F2305C028F7&index=14
![量子コンピュータ授業 #14 幾何学符号 山口文子]
(http://img.youtube.com/vi/NplMhUq4G8g/0.jpg)
量子コンピュータ授業 #15 誤り自動訂正、抑制 山口文子
https://www.youtube.com/watch?v=W9VWjZtTRCU&list=PLB1324F2305C028F7&index=15
![量子コンピュータ授業 #15 誤り自動訂正、抑制 山口文子]
(http://img.youtube.com/vi/W9VWjZtTRCU/0.jpg)
参考文献
1
1-1
Quantum Computation and Quantum Information, M.A. Nielsen, I.L. Chuang, Cambridge University Press, 2000
1-2
Pysical Review A 65, 012320, 2001, N.D. Memin
1-3
EXPERIMENTAL QUANTUM COMPUTATION WITH NUCLEAR SPINS IN LIQUID SOLUTION, L.M.K. Vandersypen, Ph.D Thesis,2001, arXiv quant-ph 0205193, https://arxiv.org/abs/quant-ph/0205193
1-4
量子コンピュータ、竹内
1-1 ref.
Bibliography
Citations with ‘arXive e-print quant-ph/xxxxxxx’ designations are available on the in- ternet at http://www.arXiv.org
D. Aharonov and M. Ben-Or. Fault tol- erant computation with constant error. In Proceedings of the Twenty-Ninth An- nual ACM Symposium on the Theory of Computing, pages 176–188, 1997.
D. Aharonov and M. Ben-Or. Fault- tolerant quantum computation with con- stant error rate. SIAM J. Comp., page to appear, 1999. arXive e-print at http://www.arXiv.org/abs/quant-ph/9906129.
D. Aharonov, M. Ben-Or, R. Impagli- azzo, and N. Nisan. Limitations of noisy reversible computation. arXive e-print http://www.arXiv.org/abs/quant-ph/9611028, 1996.
L. Adleman, J. Demarrais, and M. A. Huang. Quantum computability. SIAM J. Comp., 26(5):1524–1540, 1997. L. M. Adleman. Molecular computation of solutions to combinatorial problems. Science, 266:1021, 1994.
L. M. Adleman. Computing with DNA. Sci. Am., 279:54–61, Aug. 1998.
L. Allen and J. H. Eberly. Optical Res- onance and Two-level Atoms. Dover, New York, 1975.
D. Aharonov. Noisy Quantum Computation. Ph.D. thesis, The Hebrew Uni- vesity, Jerusalem, 1999.
D. Aharonov. Quantum computation. In D. Stauffer, editor, Annual Reviews of Computational Physics VI. World Sci- entific, Singapore, 1999.
D. Aharonov, A. Kitaev, and N. Nisan. Quantum circuits with mixed states. STOC 1997, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9806029.
H. Araki and E. H. Lieb. Entropy inequal- ities. Comm. Math. Phys., 18:160–170, 1970.
D. S. Abrams and S. Lloyd. Simulation of many-body Fermi systems on a quantum computer. Phys. Rev. Lett., 79(13):2586–2589, 1997. arXive e-print http://www.arXiv.org/abs/quant-ph/9703054.
A. Ashikhmin and S. Lytsin. Upper bounds on the size of quantum codes. IEEE Trans. Inf. Theory, 45(4):1206– 1215, 1999.
P. M. Alberti. A note on the transition- probability over c-* algebras. Lett. in Math. Phys., 7(1):25–32, 1983.
A. Ambainis. Quantum lower bounds by quantum arguments. arXive e-print http://www.arXiv.org/abs/quant-ph/0002066, 2000.
T. Ando. Concavity of certain maps on positive definite matrices and applications to Hadamard products. Linear Algebra Appl., 26:203–241, 1979.
A. Ashikhmin. Remarks on bounds for quantum codes. arXive e-print http://www.arXiv.org/abs/quant-ph/9705037, 1997.
E. Barton. A reversible computer us- ing conservative logic. Unpublished MIT 6.895 term paper, 1978.
C. H. Bennett and G. Brassard. Quan- tum cryptography: Public key distribution and coin tossing. In Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, pages 175–179, IEEE, New York, 1984. Banga- lore, India, December 1984.
C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin. Experimen- tal quantum cryptography. J. Cryptology, 5:3–28, 1992.
E. Biham, M. Boyer, G. Brassard, J. van de Graaf, and T. Mor. Security of quantum key distribution against all col- lective attacks. arXive e-print http://www.arXiv.org/abs/quant-ph/9801022, 1998.
C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani. Strengths and weak- nesses of quantum computing. SIAM J. Comput., 26(5):1510–1523, 1997. arXive e-print http://www.arXiv.org/abs/quant-ph/9701001.
C. H. Bennett, G. Brassard, C. Cre ́peau, R. Jozsa, A. Peres, and W. Wootters. Tele- porting an unknown quantum state via dual classical and EPR channels. Phys. Rev. Lett., 70:1895–1899, 1993.
A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter. Elementary gates for quantum computation. Phys. Rev. A, 52:3457–3467, 1995. arXive e-print http://www.arXiv.org/abs/quant-ph/9503016.
R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf. Quantum lower bounds by polynomials. In Pro- ceedings of the 39th Annual Sympo- sium on Foundations of Computer Sci- ence (FOCS’98), pages 352–361, IEEE, Los Alamitos, California, November 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9802049.
C. H. Bennett, G. Brassard, C. Cre ́peau, and U. M. Maurer. Generalized privacy amplification. IEEE Trans. Inf. Theory, 41:1915–1923, 1995.
C. H. Bennett, G. Brassard, and A. K. Ek- ert. Quantum cryptography. Sci. Am., 267(4):50, Oct. 1992.
M. Boyer, G. Brassard, P. Høyer, and A. Tapp. Tight bounds on quantum searching. Fortsch. Phys. – Prog. Phys., 46(4–5):493–505, 1998.
D. Boschi, S. Branca, F. D. Martini, L. Hardy, and S. Popescu. Experimen- tal realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolski-Rosen channels. Phys. Rev. Lett., 80:1121–1125, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9710013.
C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett., 76:722, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9511027.
C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher. Concentrating partial entanglement by local operations. Phys. Rev. A, 53(4):2046–2052, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9511030.
C. H. Bennett, G. Brassard, and J. M. Robert. Privacy amplification by public discussion. SIAM J. Comp., 17:210–229, 1988.
D. Beckman, A. N. Chari, S. Devabhak- tuni, and J. Preskill. Efficient networks for quantum factoring. Phys. Rev. A, 54(2):1034, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9602016.
H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa, and B. Schumacher. Noncom- muting mixed states cannot be broad- cast. Phys. Rev. Lett., 76(15):2828– 2821, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9511010.
S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack. Separability of very noisy mixed states and implications for NMR quantum comput- ing. Phys. Rev. Lett., 83(5):1054–1057, 1999.
G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch. Quantum logic gates in optical lattices. Physical Review Letters, 82:1060–1063, 1999.
C. H. Bennett and D. P. DiVincenzo. Quantum information and computation. Nature, 404:247–55, 2000. J.L.Balca ́zar,J.Diaz,andJ.Gabarro ́. Structural Complexity, Volume I. Springer-Verlag, Berlin, 1988. J.L.Balca ́zar,J.Diaz,andJ.Gabarro ́. Structural Complexity, Volume II. Springer-Verlag, Berlin, 1988.
R. G. Brewer, R. G. DeVoe, and R. Kallenbach. Planar ion microtraps. Phys. Rev. A, 46(11):R6781–4, 1992.
C. H. Bennett, D. P. DiVincenzo, and J. A. Smolin. Capacities of quan- tum erasure channels. Phys. Rev. Lett., 78(16):3217–3220, 1997. arXive e-print http://www.arXiv.org/abs/quant-ph/9701015.
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters. Mixed state entanglement and quantum error correction. Phys. Rev. A, 54:3824, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9604024.
J. S. Bell. On the Einstein-Podolsy- Rosen paradox. Physics, 1:195–200, 1964. Reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, Cambridge, 1987.
C. H. Bennett. Logical reversibility
of computation. IBM J. Res. Dev., 17(6):525–32, 1973.
P. Benioff. The computer as a physical system: A microscopic quantum mechan- ical Hamiltonian model of computers as represented by Turing machines. J. Stat. Phys., 22(5):563–591, 1980.
C. H. Bennett. The thermodynamics of computation - a review. Int. J. Theor. Phys., 21:905–40, 1982.
C. H. Bennett. Demons, engines and the second law. Sci. Am., 295(5):108, 1987. C. H. Bennett. Time-space trade-offs for reversible computation. SIAM J. Com- put., 18:766–776, 1989.
C. H. Bennett. Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett., 68(21):3121–3124, 1992.
T. Beth. Methoden der Schnellen Fouriertransformation. Teubner, Leipzig, 1984.
S. L. Braunstein, C. A. Fuchs, D. Gottes- man, and H. Lo. A quantum analog of Huffman coding. arXive e-print http://www.arXiv.org/abs/quant-ph/9805080, 1998.
H. Barnum, C. A. Fuchs, R. Jozsa, and B. Schumacher. General fidelity limit for quantum channels. Phys. Rev. A, 54:4707, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9603014.
R. Bhatia. Matrix Analysis. Springer- Verlag, New York, 1997.
G. Brassard, P. Høyer, and A. Tapp. Quantum counting. arXive e-print http://www.arXiv.org/abs/quant-ph/9805082, 1998.
V. B. Braginsky and F. Y. Khahili. Quan- tum Measurement. Cambridge Univer- sity Press, Cambridge, 1992.
S. L. Braunstein and H. J. Kimble. Tele- portation of continuous quantum vari- ables. Phys. Rev. Lett., 80:869–72, 1998. S. B. Bravyi and A. Y. Kitaev. Quantum codes on a lattice with boundary. arXive e-print http://www.arXiv.org/abs/quant-ph/9811052, 1998.
S. L. Braunstein and H. J. Kimble. Dense coding for continuous variables. arXive e-print http://www.arXiv.org/abs/quant-ph/9910010, 1999.
D. Bacon, J. Kempe, D. A. Lidar, and K. B. Whaley. Universal fault- tolerant computation on decoherence- free subspaces. arXive e-print http://www.arXiv.org/abs/quant-ph/9909058, 1999.
H. Barnum, E. Knill, and M. A. Nielsen. On quantum fidelities and channel capacities. arXive e-print http://www.arXiv.org/abs/quant-ph/9809010, 1998.
D. Boneh and R. J. Lipton. Quantum cryptoanalysis of hidden linear functions (extended abstract). In Don Coppersmith, editor, Lecture notes in computer sci- ence — Advances in Cryptology — CRYPTO’95, pages 424–437, Springer- Verlag, Berlin, 1995.
P. O. Boykin, T. Mor, M. Pulver, V. Roy- chowdhury, and F. Vatan. On univer- sal and fault-tolerant quantum comput- ing. arXive e-print http://www.arXiv.org/abs/quant-ph/9906054, 1999.
H. Barnum, M. A. Nielsen, and B. W. Schumacher. Information trans- mission through a noisy quantum channel. Phys. Rev. A, 57:4153, 1998.
D. Bohm. Quantum Theory. Prentice- Hall, Englewood Cliffs, New Jersey, 1951. S. M. Barnett and S. J. D. Phoenix. Information-theoretic limits to quantum cryptography. Phys. Rev. A, 48(1):R5– R8, 1993.
D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger. Experimental quantum teleportation. Na- ture, 390(6660):575–579, 1997.
D. S. Bethune and W. P. Risk. An au- tocompensating quantum key distribution system using polarization splitting of light. In IQEC ’98 Digest of Postdeadline Pa- pers, pages QPD12–2, Optical Society of America, Washington, DC, 1998.
D. S. Bethune and W. P. Risk. An auto- compensating fiber-optic quantum cryp- tography system based on polarization splitting of light. J. Quantum Electron- ics, 36(3):100, 2000.
G. Brassard. A bibliography of quantum cryptography. Universite ́ de Montre ́al preprint, pages 1–10, 3 December 1993. A preliminary version of this appeared in Sigact News, vol. 24(3), 1993, pages 16- 20.
S. L. Braunstein. Error correction for con- tinuous quantum variables. Phys. Rev. Lett., 80:4084–4087, 1998. arXive e- print http://www.arXiv.org/abs/quant-ph/9711049.
G. Brassard and L. Salvail. Secret-key reconciliation by public discussion. In T. Helleseth, editor, Lecture Notes in Computer Science: Advances in Cryp- tology – EUROCRYPT’93, Volume
765, pages 410–423, Springer-Verlag, New York, 1994.
C. H. Bennett and P. W. Shor. Quan- tum information theory. IEEE Trans. Inf. Theory, 44(6):2724–42, 1998.
H. Barnum, J. A. Smolin, and B. Ter- hal. Quantum capacity is properly de- fined without encodings. Phys. Rev. A, 58(5):3496–3501, 1998.
B. M. Boghosian and W. Taylor. Sim- ulating quantum mechanics on a quan- tum computer. arXive e-print http://www.arXiv.org/abs/quant-ph/9701019, 1997.
E. Bernstein and U. Vazirani. Quantum complexity theory. SIAM J. Comput., 26(5):1411–1473, 1997. arXive e-print http://www.arXiv.org/abs/quant-ph/9701001.
C. H. Bennett and S. J. Wiesner. Commu- nication via one- and two-particle oper- ators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett., 69(20):2881–2884, 1992.
N. J. Cerf, C. Adami, and P. Kwiat. Op- tical simulation of quantum logic. Phys. Rev. A, 57:R1477, 1998.
C. M. Caves. Quantum error correction and reversible operations. Journal of Su- perconductivity, 12(6):707–718, 1999.
R. Cleve and D. P. DiVincenzo. Schu- macher’s quantum data compression as a quantum computation. Phys. Rev. A, 54:2636, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9603009.
R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca. Quantum algorithms revisited. Proc. R. Soc. London A, 454(1969):339– 354, 1998.
D. G. Cory, A. F. Fahmy, and T. F. Havel. Ensemble quantum computing by NMR spectroscopy. Proc. Nat. Acad. Sci. USA, 94:1634–1639, 1997.
I. L. Chuang, N. Gershenfeld, and M. Kubinec. Experimental implementa- tion of fast quantum searching. Phys. Rev. Lett., 18(15):3408–3411, 1998.
I. L. Chuang, N. Gershenfeld, M. G. Ku- binec, and D. W. Leung. Bulk quan- tum computation with nuclear-magnetic- resonance: theory and experiment. Proc. R. Soc. London A, 454(1969):447–467, 1998.
P. R. Chernoff. Note on product formu- las for operator semigroups. J. Functional Analysis, 2:238–242, 1968.
M.-D. Choi. Completely positive linear maps on complex matrices. Linear Al- gebra and Its Applications, 10:285–290, 1975.
J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 49:1804–1807, 1969.
A. Church. An unsolvable problem of el- ementary number theory. Am. J. Math. (reprinted in [Dav65]), 58:345, 1936. I. Csisza ́r and J. Ko ̈rner. Information Theory: Coding Theorems for Discrete Memoryless Systems. Academic Press, New York, 1981.
A. O. Caldeira and A. J. Leggett. Quan- tum tunnelling in a dissipative system. Ann. Phys., 149(2):374–456, 1983.
M. Clausen. Fast generalized Fourier transforms. Theor. Comput. Sci., 67:55– 63, 1989.
R. Cleve. The query complexity of order-finding. arXive e-print http://www.arXiv.org/abs/quant-ph/9911124, 1999.
T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, Mass., 1990.
C. Cachin and U. M. Maurer. Link- ing information reconciliation and privacy amplification. J. Cryptology, 10:97–110, 1997.
I. L. Chuang and D. Modha. Reversible arithmetic coding for quantum data com- pression. IEEE Trans. Inf. Theory, 46(3):1104, May 2000.
D. G. Cory, W. Mass, M. Price, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo. Experimental quan- tum error correction. arXive e-print http://www.arXiv.org/abs/quant-ph/9802018, 1998.
I. L. Chuang and M. A. Nielsen. Prescrip- tion for experimental determination of the dynamics of a quantum black box. J. Mod. Opt., 44(11-12):2455–2467, 1997. arXive e-print http://www.arXiv.org/abs/quant-ph/9610001.
J. H. Conway. Unpredictable iterations. In
Proceedings of the Number Theory Con- ference, pages 49–52, Boulder, Colorado, 1972.
J. H. Conway. Fractran: a simple universal programming language. In T. M. Cover and B. Gopinath, editors, Open Prob- lems in Communication and Computa- tion, pages 4–26, Springer-Verlag, New York, 1986.
S. A. Cook. The complexity of theorem- proving procedures. In Proc. 3rd Ann. ACM Symp. on Theory of Computing, pages 151–158, Association for Comput- ing Machinery, New York, 1971.
D. Coppersmith. An approximate Fourier transform useful in quantum factoring. IBM Research Report RC 19642, 1994. J. I. Cirac, T. Pellizzari, and P. Zoller. En- forcing coherent evolution in dissipative quantum dynamics. Science, 273:1207, 1996.
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane. Quantum error correction and orthogonal geometry. Phys. Rev. Lett., 78:405–8, 1997.
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane. Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theory, 44(4):1369–1387, 1998.
A. R. Calderbank and P. W. Shor. Good quantum error-correcting codes ex- ist. Phys. Rev. A, 54:1098, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9512032.
R. A. Campos, B. E. A. Saleh, and M. C. Tiech. Quantum-mechanical loss- less beamsplitters: SU(2) symmetry and photon statistics. Phys. Rev. A, 40:1371, 1989.
T. M. Cover and J. A. Thomas. Elements of Information Theory. John Wiley and Sons, New York, 1991.
C. Cohen-Tannoudji, B. Diu, and F. Laloe ̈. Quantum Mechanics, Vol. I.
John Wiley and Sons, New York, 1977. [CTDL77b] C. Cohen-Tannoudji, B. Diu, and F. Laloe ̈. Quantum Mechanics, Vol. II.
John Wiley and Sons, New York, 1977. I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd. Experimental realization of a quantum algorithm. Nature, 393(6681):143–146, 1998.
H. F. Chau and F. Wilczek. Simple re- alization of the Fredkin gate using a se- ries of two-body operators. Phys. Rev. Lett., 75(4):748–50, 1995. arXive e-print http://www.arXiv.org/abs/quant-ph/9503005.
I. L. Chuang and Y. Yamamoto. Sim- ple quantum computer. Phys. Rev. A, 52:3489–3496, 1995. arXive e-print http://www.arXiv.org/abs/quant-ph/9505011.
J. I. Cirac and P. Zoller. Quantum compu tations with cold trapped ions. Phys. Rev.
Lett., 74:4091, 1995.
M. D. Davis. The Undecidable. Raven Press, Hewlett, New York, 1965.
E. B. Davies. Quantum Theory of Open Systems. Academic Press, London, 1976. D. Deutsch, A. Barenco, and A. Ek- ert. Universality in quantum computation. Proc. R. Soc. London A, 449(1937):669– 677, 1995.
D. Deutsch. Uncertainty in quan- tum measurements. Phys. Rev. Lett., 50(9):631–633, 1983.
D. Deutsch. Quantum theory, the Church-Turing Principle and the uni- versal quantum computer. Proc. R. Soc. Lond. A, 400:97, 1985.
D. Deutsch. Quantum computational networks. Proc. R. Soc. London A, 425:73, 1989.
L.-M. Duan and G.-C. Guo. Probabilistic cloning and identification of linearly independent quantum states. Phys. Rev. Lett., 80:4999–5002, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9804064.
W. Diffie and M. Hellman. New directions in cryptography. IEEE Trans. Inf. Theory, IT-22(6):644–54, 1976.
C. Du ̈rr and P. Høyer. A quantum algorithm for finding the minimum. arXive e-print http://www.arXiv.org/abs/quant-ph/9607014, 1996.
D. Dieks. Communication by EPR devices. Phys. Lett. A, 92(6):271–272, 1982. D. P. DiVincenzo. Quantum computa- tion. Science, 270:255, 1995.
D. P. DiVincenzo. Two-bit gates are uni- versal for quantum computation. Phys. Rev. A, 51(2):1015–1022, 1995.
D. P. DiVincenzo. Quantum gates and cir- cuits. Proc. R. Soc. London A, 454:261– 276, 1998.
D. Deutsch and R. Jozsa. Rapid solu- tion of problems by quantum computa- tion. Proc. R. Soc. London A, 439:553, 1992.
W. Diffie and S. Landau. Privacy on the Line: the Politics of Wiretapping and Encryption. MIT Press, Cambridge Mas- sachusetts, 1998.
L. Davidovich, A. Maali, M. Brune, J. M. Raimond, and S. Haroche. Phys. Rev. Lett., 71:2360, 1993.
P. Diaconis and D. Rockmore. Efficient computation of the Fourier transform
on finite groups. J. Amer. Math. Soc., 3(2):297–332, 1990.
L. Davidovich, J. M. Raimond, M. Brune, and S. Haroche. Phys. Rev. A, 36:3771, 1987.
P. Domokos, J. M. Raimond, M. Brune, and S. Haroche. Simple cavity-QED two-bit universal quantum logic gate: The principle and expected performances. Phys. Rev. Lett., 52:3554, 1995.
D. P. DiVincenzo and P. W. Shor. Fault-tolerant error correction with effi- cient quantum codes. Phys. Rev. Lett., 77:3260, 1996.
D. P. DiVincenzo, P. W. Shor, and J. Smolin. Quantum-channel capacities of very noisy channels. Phys. Rev. A, 57(2):830–839, 1998.
S. Earnshaw. On the nature of the molec- ular forces which regulate the constitution of the luminiferous ether. Trans. Camb. Phil. Soc., 7:97–112, 1842.
R. R. Ernst, G. Bodenhausen, and A. Wokaun. Principles of Nuclear Mag- netic Resonance in One and Two Dimen- sions. Oxford University Press, Oxford, 1987.
M. Ettinger and P. Høyer. On quan- tum algorithms for noncommutative hid- den subgroups. In Symposium on The- oretical Aspects in Computer Science. University of Trier, 1999. arXive e-print http://www.arXiv.org/abs/quant-ph/9807029.
M. Ettinger, P. Høyer, and E. Knill. Hid- den subgroup states are almost orthogo- nal. arXive e-print http://www.arXiv.org/abs/quant-ph/9901034, 1999.
A. K. Ekert, B. Huttner, G. M. Palma, and A. Peres. Eavesdropping on quantum- cryptographical systems. Phys. Rev. A, 50(2):1047–1056, 1994.
A. Ekert and R. Jozsa. Quantum computation and Shor’s factoring algorithm. Rev. Mod. Phys., 68:733, 1996.
A. Ekert and R. Jozsa. Quantum algo- rithms: Entanglement enhanced informa- tion processing. Proc. R. Soc. London A, 356(1743):1769–82, Aug. 1998. arXive e- print http://www.arXiv.org/abs/quant-ph/9803072.
A. K. Ekert. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett., 67(6):661–663, 1991.
A. Ekert and C. Macchiavello. Error cor- rection in quantum communication. Phys.
Rev. Lett., 77:2585, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9602022.
A. Einstein, B. Podolsky, and N. Rosen. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev., 47:777–780, 1935.
H. Epstein. Commun. Math. Phys., 31:317–325, 1973.
M. Fannes. A continuity property of the entropy density for spin lattice sys- tems. Commun. Math. Phys., 31:291– 294, 1973.
C. A. Fuchs and C. M. Caves. Ensemble- dependent bounds for accessible informa- tion in quantum mechanics. Phys. Rev. Lett., 73(23):3047–3050, 1994.
W. Feller. An Introduction to Probabil- ity Theory and its Applications, Vol- ume 1. Wiley, New York, 1968.
W. Feller. An Introduction to Probabil- ity Theory and its Applications, Vol- ume 2. Wiley, New York, 1968.
R. P. Feynman. Simulating physics with computers. Int. J. Theor. Phys., 21:467, 1982.
E. Farhi and S. Gutmann. An analog ana- logue of a digital quantum computation. Phys. Rev. A, 57(4):2403–2406, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9612026.
R. P. Feynman, R. B. Leighton, and M. Sands. Volume III of The Feynman Lectures on Physics. Addison-Wesley, Reading, Mass., 1965.
R. P. Feynman, R. B. Leighton, and M. Sands. Volume I of The Feynman Lectures on Physics. Addison-Wesley, Reading, Mass., 1965.
M. H. Freedman and D. A. Meyer. Pro- jective plane and planar quantum codes. arXive e-print http://www.arXiv.org/abs/quant-ph/9810055, 1998. A.Fa ̈sslerandE.Stiefel.GroupTheo- retical Methods and Their Applications. Birkhau ̈ ser, Boston, 1992.
A. Furusawa, J. L. Sørensen, S. L. Braun- stein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik. Unconditional quantum tele-portation. Science, 282:706–709, 1998. E. Fredkin and T. Toffoli. Conservative logic. Int. J. Theor. Phys., 21(3/4):219– 253, 1982.
C. A. Fuchs. Distinguishability and Ac- cessible Information in Quantum The- ory. Ph.D. thesis, The University of New Mexico, Albuquerque, NM, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9601020.
C. A. Fuchs. Nonorthogonal quantum states maximize classical information ca- pacity. Phys. Rev. Lett., 79(6):1162– 1165, 1997.
C. A. Fuchs and J. van de Graaf. Cryp- tographic distinguishability measures for quantum-mechanical states. IEEE Trans. Inf. Theory, 45(4):1216–1227, 1999.
C. W. Gardiner. Quantum Noise. Springer-Verlag, Berlin, 1991.
N. Gershenfeld and I. L. Chuang. Bulk spin resonance quantum computation. Science, 275:350, 1997.
D. Gottesman and I. L. Chuang. Quantum teleportation is a univer- sal computational primitive. Nature, 402:390–392, 1999. arXive e-print http://www.arXiv.org/abs/quant-ph/9908010.
M. R. Garey and D. S. Johnson. Com- puters and Intractibility. W. H. Freeman and Company, New York, 1979.
R. B. Griffiths and C.-S. Niu. Semi- classical Fourier transform for quan- tum computation. Phys. Rev. Lett., 76(17):3228–3231, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9511007.
J. P. Gordon. Noise at optical frequencies; information theory. In P. A. Miles, edi- tor, Quantum Electronics and Coherent Light, Proceedings of the International School of Physics ‘Enrico Fermi’ XXXI, Academic Press, New York, 1964.
D. Gottesman. Class of quantum error- correcting codes saturating the quantum Hamming bound. Phys. Rev. A, 54:1862, 1996.
D. Gottesman. Stabilizer Codes and Quantum Error Correction. Ph.D. the- sis, California Institute of Technology, Pasadena, CA, 1997.
D. Gottesman. Fault-tolerant quantum computation with higher-dimensional systems. arXive e-print http://www.arXiv.org/abs/quant-ph/9802007, 1998.
D. Gottesman. Theory of fault-tolerant quantum computation. Phys. Rev. A, 57(1):127–137, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9702029.
D. Gottesman and J. Preskill. The Hitchiker’s guide to the threshold theo- rem. Eternally in preparation, 1:1–9120, 2010.
L. Grover. In Proc. 28th Annual ACM
Symposium on the Theory of Compu- tation, pages 212–219, ACM Press, New York, 1996.
L. K. Grover. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett., 79(2):325, 1997. arXive e-print http://www.arXiv.org/abs/quant-ph/9706033.
J. Gruska. Quantum Computing. McGraw-Hill, London, 1999.
G. R. Grimmett and D. R. Stirzaker. Probability and Random Processes. Clarendon Press, Oxford, 1992.
R. J. Hughes, D. M. Alde, P. Dyer, G. G. Luther, G. L. Morgan, and M. Schauer. Quantum cryptography. Contemp. Phys., 36(3):149–163, 1995. arXive e-print http://www.arXiv.org/abs/quant-ph/9504002.
P. R. Halmos. Finite-dimensional Vector Spaces. Van Nostrand, Princeton, N.J., 1958.
M. Hammermesh. Group Theory and its Application to Physical Problems. Dover, New York, 1989.
J. L. Hennessey, D. Goldberg, and D. A. Patterson. Computer Architec- ture: A Quantitative Approach. Aca- demic Press, New York, 1996.
M. Horodecki, P. Horodecki, and R. Horodecki. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A, 223(1-2):1–8, 1996.
M. Horodecki, P. Horodecki, and R. Horodecki. Mixed-state entanglement and distillation: is there a ‘bound’ en- tanglement in nature? Phys. Rev. Lett., 80(24):5239–5242, 1998.
M. Horodecki, P. Horodecki, and R. Horodecki. General teleportation channel, singlet fraction, and quasidistil- lation. Phys. Rev. A, 60(3):1888–1898, 1999.
M. Horodecki, P. Horodecki, and R. Horodecki. Limits for entanglement measures. arXive e-print http://www.arXiv.org/abs/quant-ph/9908065, 1999.
P. Horodecki, M. Horodecki, and R. Horodecki. Bound entanglement can be activated. Phys. Rev. Lett., 82(5):1056–1059, 1999.
R. A. Horn and C. R. Johnson. Matrix Analysis. Cambridge University Press, Cambridge, 1985.
R. A. Horn and C. R. Johnson. Topics in Matrix Analysis. Cambridge University Press, Cambridge, 1991.
P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters. Classical information capacity of a quan- tum channel. Phys. Rev. A, 54:1869, 1996.
L. P. Hughston, R. Jozsa, and W. K. Wootters. A complete classi- fication of quantum ensembles having a given density matrix. Phys. Lett. A, 183:14–18, 1993.
K.-E. Hellwig and K. Kraus. Pure op- erations and measurements. Commun. Math. Phys., 11:214–220, 1969.
K.-E. Hellwig and K. Kraus. Operations and measurements. II. Commun. Math. Phys., 16:142–147, 1970.
D. R. Hofstadter. Go ̈ del, Escher, Bach: an Eternal Golden Braid. Basic Books, New York, 1979.
A. S. Holevo. Statistical problems in quantum physics. In Gisiro Maruyama and Jurii V. Prokhorov, editors, Proceed- ings of the Second Japan–USSR Sym- posium on Probability Theory, pages 104–119, Springer-Verlag, Berlin, 1973. Lecture Notes in Mathematics, vol. 330. A. S. Holevo. Capacity of a quantum communications channel. Problems of Inf. Transm., 5(4):247–253, 1979.
A. S. Holevo. The capacity of the quan- tum channel with general signal states. IEEE Trans. Inf. Theory, 44(1):269– 273, 1998.
M. Horodecki. Limits for compression of quantum information carried by en- sembles of mixed states. Phys. Rev. A, 57:3364–3369, 1997.
A. G. Huibers, M. Switkes, C. M. Mar- cus, K. Campman, and A. C. Gossard. Dephasing in open quantum dots. Phys. Rev. Lett., 82:200, 1998.
G. H. Hardy and E. M. Wright. An In- troduction to the Theory of Numbers, Fourth Edition. Oxford University Press, London, 1960.
A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small. Quantum information processing using quantum dot spins and cavity qed. Phys. Rev. Lett., 83(20):4204–7, 1999.
A. Imamoglu and Y. Yamamoto. Turn- stile device for heralded single pho- tons: Coulomb blockade of electron and hole tunneling in quantum confined p-i-n heterojunctions. Phys. Rev. Lett., 72(2):210–13, 1994.
D. James. The theory of heating of the quantum ground state of trapped ions. arXive e-print http://www.arXiv.org/abs/quant-ph/9804048, 1998.
E. T. Jaynes. Information theory and statistical mechanics. ii. Phys. Rev., 108(2):171–190, 1957.
J. A. Jones and M. Mosca. Implemen- tation of a quantum algorithm to solve Deutsch’s problem on a nuclear magnetic resonance quantum computer. arXive e- print http://www.arXiv.org/abs/quant-ph/9801027, 1998.
J. A. Jones, M. Mosca, and R. H. Hansen. Implementation of a quantum search algorithm on a nuclear magnetic res- onance quantum computer. Nature, 393(6683):344, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9805069.
K. R. W. Jones. Fundamental limits upon the measurement of state vectors. Phys. Rev. A, 50:3682–3699, 1994.
R. Jozsa. Fidelity for mixed quantum states. J. Mod. Opt., 41:2315–2323, 1994. R. Jozsa. Quantum algorithms and the Fourier transform. arXive e-print http://www.arXiv.org/abs/quant-ph/9707033, 1997.
D. Jonathan and M. B. Plenio. Entanglement-assisted local manipu- lation of pure states. Phys. Rev. Lett., 83:3566–3569, 1999.
R. Jozsa and B. Schumacher. A new proof of the quantum noiseless coding theorem. J. Mod. Opt., 41:2343–2349, 1994.
D. Kahn. Codebreakers: the Story of Se- cret Writing. Scribner, New York, 1996. B. Kane. A silicon-based nuclear spin quantum computer. Nature, 393:133– 137, 1998.
R. M. Karp. Reducibility among com- binatorial problems. In Complexity of Computer Computations, pages 85–103, Plenum Press, New York, 1972.
E. Knill, I. Chuang, and R. Laflamme. Effective pure states for bulk quantum computation. Phys. Rev. A, 57(5):3348– 3363, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9706053.
A. Y. Kitaev. Quantum measurements and the Abelian stabilizer problem. arXive e- print http://www.arXiv.org/abs/quant-ph/9511026,, 1995.
A. Y. Kitaev. Fault-tolerant quantum computation by anyons. arXive e-print http://www.arXiv.org/abs/quant-ph/9707021, 1997.
A. Y. Kitaev. Quantum computations: algorithms and error correction. Russ. Math. Surv., 52(6):1191–1249, 1997.
A. Y. Kitaev. Quantum error correction with imperfect gates. In A. S. Holevo O. Hirota and C. M. Caves, edi- tors, Quantum Communication, Com- puting, and Measurement, pages 181– 188, Plenum Press, New York, 1997.
S. Kullback and R. A. Leibler. On in- formation and sufficiency. Ann. Math. Stat., 22:79–86, 1951.
E. Knill and R. Laflamme. A theory of quantum error-correcting codes. Phys. Rev. A, 55:900, 1997. arXive e-print http://www.arXiv.org/abs/quant-ph/9604034.
E. Knill and R. Laflamme. Quantum com- putation and quadratically signed weight enumerators. arXive e-print http://www.arXiv.org/abs/quant-ph/9909094, 1999.
O. Klein. Z. Phys., 72:767–775, 1931.
E. Knill, R. Laflamme, and L. Viola. Theory of quantum error correction for general noise. arXive e-print http://www.arXiv.org/abs/quant-ph/9908066, 1999.
E. Knill, R. Laflamme, and W. H. Zurek. Resilient quantum computation. Science, 279(5349):342–345, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9702058.
E. Knill, R. Laflamme, and W. H. Zurek. Resilient quantum computation: error models and thresholds. Proc. R. Soc. London A, 454(1969):365–384, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9702058.
P. G. Kwiat, J. R. Mitchell, P. D. D. Schwindt, and A. G. White. Grover’s search algorithm: An optical approach. arXive e-print http://www.arXiv.org/abs/quant-ph/9905086, 1999.
E. Knill. Approximating quantum circuits. arXive e-print http://www.arXiv.org/abs/quant-ph/9508006, 1995.
D. E. Knuth. Fundamental Algorithms 3rd Edition, Volume 1 of The Art of Computer Programming. Addison- Wesley, Reading, Massachusetts, 1997. D. E. Knuth. Seminumerical Algorithms 3rd Edition, Volume 2 of The Art of Computer Programming. Addison- Wesley, Reading, Massachusetts, 1998. D. E. Knuth. Sorting and Searching 2nd Edition, Volume 3 of The Art of Computer Programming. Addison- Wesley, Reading, Massachusetts, 1998. N. Koblitz. A Course in Number Theory and Cryptography. Springer-Verlag,
New York, 1994.
C. King and M. B. Ruskai. Minimal en- tropy of states emerging from noisy quan- tum channels. arXive e-print http://www.arXiv.org/abs/quant-ph/9911079, 1999.
K. Kraus. States, Effects, and Opera- tions: Fundamental Notions of Quan- tum Theory. Lecture Notes in Physics, Vol. 190. Springer-Verlag, Berlin, 1983. K. Kraus. Complementary observables and uncertainty relations. Phys. Rev. D, 35(10):3070–3075, 1987.
P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff. Absolute efficiency and time-response measurement of single-photon detectors. Appl. Opt., 33(10):1844–1853, 1994.
M. Kitagawa and M. Ueda. Nonlinear- interferometric generation of number- phase correlated Fermion states. Phys. Rev. Lett., 67(14):1852, 1991.
L. Landau. Das da ̈mpfungsproblem in der wellenmechanik. Z. Phys., 45:430–441, 1927.
R. Landauer. Irreversibility and heat gen- eration in the computing process. IBM J. Res. Dev., 5:183, 1961.
S. Lloyd and S. Braunstein. Quantum computation over continuous variables. Phys. Rev. Lett., 82:1784–1787, 1999. arXive e-print http://www.arXiv.org/abs/quant-ph/9810082.
D. A. Lidar, D. A. Bacon, and K. B. Wha- ley. Concatenating decoherence free sub- spaces with quantum error correcting codes. Phys. Rev. Lett., 82(22):4556– 4559, 1999.
H. Lo and H. F. Chau. Uncondi- tional security of quantum key distribu- tion over arbitrarily long distances. Sci- ence, 283:2050–2056, 1999. arXive e- print http://www.arXiv.org/abs/quant-ph/9803006.
D. A. Lidar, I. L. Chuang, and K. B. Whaley. Decoherence-free sub- spaces for quantum computation. Phys. Rev. Lett., 81(12):2594–2597, 1998.
D. Loss and D. P. DiVincenzo. Quantum computation with quantum dots. Phys. Rev. A, 57:120–126, 1998.
Y. Lecerf. Machines de Turing re ́versibles. Comptes Rendus, 257:2597– 2600, 1963.
U. Leonhardt. Measuring the Quantum State of Light. Cambridge University
Press, New York, 1997.
L. Levin. Universal sorting problems.
77:198, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9602019.
D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto. Approximate quantum error correction can lead to better codes. Phys. Rev. A, 56:2567–2573, 1997. arXive e-print http://www.arXiv.org/abs/quant-ph/9704002.
H. Lo. A simple proof of the uncondi- tional security of quantum key distribu- tion. arXive e-print http://www.arXiv.org/abs/quant-ph/9904091, 1999.
J. S. Lomont. Applications of Finite Groups. Dover, New York, 1987.
W. H. Louisell. Quantum Statistical Properties of Radiation. Wiley, New York, 1973.
H.-K. Lo and S. Popescu. Concentrating local entanglement by local actions – be- yond mean values. arXive e-print http://www.arXiv.org/abs/quant-ph/9707038, 1997.
N. Linden and S. Popescu. Good dynam- ics versus bad kinematics. Is entangle- ment needed for quantum computation? arXive e-print http://www.arXiv.org/abs/quant-ph/9906008, 1999.
O. E. Lanford and D. Robinson. Mean en- tropy of states in quantum-statistical me- chanics. J. Math. Phys., 9(7):1120–1125, 1968.
E. H. Lieb and M. B. Ruskai. A funda- mental property of quantum-mechanical entropy. Phys. Rev. Lett., 30(10):434– 436, 1973.
E. H. Lieb and M. B. Ruskai. Proof of the strong subadditivity of quantum mechan- ical entropy. J. Math. Phys., 14:1938– 1941, 1973.
H. Leff and R. Rex. Maxwell’s De- mon: Entropy, Information, Comput- ing. Princeton University Press, Prince- ton, NJ, 1990.
L. J. Landau and R. F. Streater. On Birkhoff theorem for doubly stochastic completely positive maps of matrix al- gebras. Linear Algebra Appl., 193:107– 127, 1993.
S. Lloyd and J. E. Slotine. Analog quan- tum error correction. Phys. Rev. Lett., 80:4088–4091, 1998.
H.-K. Lo, T. Spiller, and S. Popescu. Quantum information and computation. World Scientific, Singapore, 1998.
M. Li, J. Tromp, and P. Vitanyi. Re- versible simulation of irreversible com-
Probl. Peredaci Inf., 9:115–116, 1973. Original in Russian. English translation in Probl. Inf. Transm. USSR 9:265–266 (1973).
E. H. Lieb. Convex trace functions and the Wigner-Yanase-Dyson conjec- ture. Ad. Math., 11:267–288, 1973.
E. H. Lieb. Bull. AMS, 81:1–13, 1975. G. Lindblad. Completely positive maps and entropy inequalities. Commun. Math. Phys., 40:147–151, 1975.
G. Lindblad. On the generators of quan- tum dynamical semigroups. Commun. Math. Phys., 48:199, 1976.
G. Lindblad. Quantum entropy and quan- tum measurements. In C. Bendjabal- lah, O. Hirota, and S. Reynaud, edi- tors, Quantum Aspects of Optical Com- munications, Lecture Notes in Physics, vol. 378, pages 71–80, Springer-Verlag, Berlin, 1991.
R. Lipton. DNA solution of hard compu- tational problems. Science, 268:542–525, 1995.
N. Linden, E. Kupce, and R. Freeman. NMR quantum logic gates for homonu- clear spin systems. arXive e-print http://www.arXiv.org/abs/quant-ph/9907003, 1999.
A. K. Lenstra and H. W. Lenstra Jr., ed- itors. The Development of the Number Field Sieve. Springer-Verlag, New York, 1993.
S. Lloyd. A potentially realizable quantum computer. Science, 261:1569, 1993.
S. Lloyd. Necessary and sufficient condi- tions for quantum computation. J. Mod. Opt., 41(12):2503, 1994.
S. Lloyd. Almost any quantum logic gate is universal. Phys. Rev. Lett., 75(2):346, 1995.
S. Lloyd. Universal quantum simulators. Science, 273:1073, 1996.
S. Lloyd. The capacity of the noisy quan- tum channel. Phys. Rev. A, 56:1613, 1997.
R. E. Ladner, N. A. Lynch, and A. L. Sel- man. A comparison of polynomial-time reducibilities. Theor. Comp. Sci., 1:103– 124, 1975.
R. Laflamme, C. Miquel, J.-P. Paz, and W. H. Zurek. Perfect quantum error correction code. Phys. Rev. Lett.,
putation by pebble games. Physica D, 120:168–176, 1998.
M. Li and P. Vitanyi. Reversibility and adiabatic computation: trading time and space for energy. Proc. R. Soc. London A, 452:769–789, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9703022.
D. W. Leung, L. M. K. Vandersypen, X. Zhou, M. Sherwood, C. Yannoni, M. Kubinec, and I. L. Chuang. Exper- imental realization of a two-bit phase damping quantum code. Phys. Rev. A, 60:1924, 1999.
Y. Manin. Computable and Uncom- putable (in Russian). Sovetskoye Radio, Moscow, 1980.
Y. I. Manin. Classical computing, quan- tum computing, and Shor’s factor- ing algorithm. arXive e-print http://www.arXiv.org/abs/quant-ph/9903008, 1999.
U. M. Maurer. Secret key agreement by public discussion from common informa- tion. IEEE Trans. Inf. Theory, 39:733– 742, 1993.
J. C. Maxwell. Theory of Heat. Long- mans, Green, and Co., London, 1871.
D. Mayers. Unconditional security in quantum cryptography. arXive e-print http://www.arXiv.org/abs/quant-ph/9802025, 1998.
M. Mosca and A. Ekert. The hidden sub- group problem and eigenvalue estimation on a quantum computer. arXive e-print http://www.arXiv.org/abs/quant-ph/9903071, 1999.
R. Merkle. Secure communications over insecure channels. Comm. of the ACM, 21:294–299, 1978.
G. L. Miller. Riemann’s hypothesis and tests for primality. J. Comput. Syst. Sci., 13(3):300–317, 1976.
G. J. Milburn. Quantum optical Fredkin gate. Phys. Rev. Lett., 62(18):2124, 1989. D. A. B. Miller. Optics for low energy communications inside digital processors: quantum detectors, sources, and modu- lators as efficient impedance converters. Opt. Lett., 14:146, 1989.
G. J. Milburn. A quantum mechanical Maxwell’s demon. Unpublished, 1996. G. J. Milburn. Scro ̈ dinger’s Machines: the Quantum Technology Reshaping Everyday Life. W. H. Freeman, New York, 1997.
G. J. Milburn. The Feynman Processor: Quantum Entanglement and the Computing Revolution. Perseus Books, Read- ing, Mass., 1998.
M. L. Minsky. Computation: finite and infinite machines. Prentice-Hall, Engle- wood Cliffs, N.J., 1967.
M. Marcus and H. Minc. A Survey of Matrix Theory and Matrix Inequali- ties. Dover, New York, 1992.
C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland. Demon- stration of a fundamental quantum logic gate. Phys. Rev. Lett., 75:4714, 1995.
A. W. Marshall and I. Olkin. Inequalities: Theory of Majorization and its Appli- cations. Academic Press, New York, 1979. J. E. Mooij, T. P. Orlando, L. Levi- tov, L. Tian, C. H. van der Waal, and S. Lloyd. Josephson persistent-current qubit. Science, 285:1036–1039, 1999.
T. Mor. No-cloning of orthogonal states in composite systems. Phys. Rev. Lett., 80:3137–3140, 1998.
M. Mosca. Quantum searching, counting and amplitude amplification by eigenvec- tor analysis. In R. Freivalds, editor, Pro- ceedings of International Workshop on Randomized Algorithms, pages 90–100, 1998.
M. Mosca. Quantum Computer Algo- rithms. Ph.D. thesis, University of Ox- ford, 1999.
R. Motwani and P. Raghavan. Random- ized Algorithms. Cambridge University Press, Cambridge, 1995.
F. J. MacWilliams and N. J. A. Sloane. The Theory of Error-correcting Codes. North-Holland, Amsterdam, 1977.
H. Maassen and J. H. B. Uffink. General- ized entropic uncertainty relations. Phys. Rev. Lett., 60(12):1103–1106, 1988.
A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone. Handbook of Applied Cryptography. CRC Press, 1996.
Bibliography 659
K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger. Dense coding in exper- imental quantum communication. Phys.
Rev. Lett., 76(25):4656–4659, 1996.
A. Muller, H. Zbinden, and N. Gisin. Quantum cryptography over 23 km in in- stalled under-lake telecom fibre. Euro- phys. Lett., 33:334–339, 1996.
M. A. Nielsen and C. M. Caves. Re- versible quantum operations and their ap- plication to teleportation. Phys. Rev. A, 55(4):2547–2556, 1997.
M. A. Nielsen, C. M. Caves, B. Schu- macher, and H. Barnum. Information- theoretic approach to quantum error cor- rection and reversible measurement. Proc. R. Soc. London A, 454(1969):277–304, 1998.
M. A. Nielsen. Quantum Information Theory. Ph.D. thesis, University of New Mexico, 1998.
M. A. Nielsen. Conditions for a class of entanglement transformations. Phys. Rev. Lett., 83(2):436–439, 1999. M. A. Nielsen. Probability distributions consistent with a mixed state. arXive e- print http://www.arXiv.org/abs/quant-ph/9909020, 1999.
M. A. Nielsen, E. Knill, and R. Laflamme. Complete quantum teleportation using nuclear magnetic resonance. Nature, 396(6706):52–55, 1998.
Y. Nakamura, Y. A. Pashkin, and J. S. Tsai. Coherent control of macro- scopic quantum states in a single-cooper- pair box. Nature, 398:786–788, 1999.
M. Ohya and D. Petz. Quantum Entropy and Its Use. Springer-Verlag, Berlin, 1993.
A. Pais. Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press, Oxford, 1982.
A. Pais. Inward Bound: Of Matter and Forces in the Physical World. Oxford University Press, Oxford, 1986.
A. Pais. Niels Bohr’s Times: In Physics, Philosophy, and Polity. Oxford Univer- sity Press, Oxford, 1991.
C. M. Papadimitriou. Computational Complexity. Addison-Wesley, Reading, Massachusetts, 1994.
R. Paturi. On the degree of polynomi- als that approximate symmetric Boolean functions (preliminary version). Proc. 24th Ann. ACM Symp. on Theory of Computing (STOC ’92), pages 468– 474, 1992.
J. F. Poyatos, J. I. Cirac, and P. Zoller. Complete characterization of a quantum process: the two-bit quantum gate. Phys. Rev. Lett., 78(2):390–393, 1997.
P. M. Platzman and M. I. Dykman. Quan- tum computing with electrons floating on liquid helium. Science, 284:1967, 1999. R. Penrose. The Emperor’s New Mind. Oxford University Press, Oxford, 1989. S. Perlis. Theory of Matrices. Addison- Wesley, Reading, Mass., 1952.
A. Peres. How to differentiate between non-orthogonal states. Phys. Lett. A, 128:19, 1988.
A. Peres. Quantum Theory: Concepts and Methods. Kluwer Academic, Dor- drecht, 1993.
A. Peres. Higher order schmidt decompo- sitions. Phys. Lett. A, 202:16–17, 1995. D. Petz. Quasi-entropies for finite quantum systems. Rep. Math. Phys., 23(1):57–65, 1986.
Physics Today Editor. Quantum cryptog- raphy defies eavesdropping. Physics To- day, page 21, November 1992.
M. B. Plenio and P. L. Knight. Realistic lower bounds for the factorization time of large numbers on a quantum computer. Phys. Rev. A, 53:2986–2990, 1996.
M. B. Plenio and P. L. Knight. The quantum-jump approach to dissipative dynamics in quantum optics. Rev. Mod. Phys., 70(1):101–144, 1998.
R. P. Poplavskii. Thermodynamical mod- els of information processing (in Russian). Usp. Fiz. Nauk, 115(3):465–501, 1975. M. Pueschel, M. Roetteler, and T. Beth. Fast quantum Fourier transforms for a class of non-abelian groups. arXive e- print http://www.arXiv.org/abs/quant-ph/9807064, 1998.
J. Preskill. Fault-tolerant quantum computation. arXive e-print http://www.arXiv.org/abs/quant-ph/9712048, 1997.
J. Preskill. Fault-tolerant quantum com- putation. In H.-K. Lo, T. Spiller, and S. Popescu, editors, Quantum informa- tion and computation. World Scientific, Singapore, 1998.
J. Preskill. Physics 229: Ad- vanced Mathematical Methods of Physics — Quantum Computa- tion and Information. California Institute of Technology, 1998. URL: http://www.theory.caltech.edu/people/preskill/ph229/ J. Preskill. Reliable quantum computers. Proc. R. Soc. London A, 454(1969):385– 410, 1998.
M. O. Rabin. Probabilistic algorithm for testing primality. J. Number Theory, 12:128–138, 1980.
H. Z. Rahim. Richard Feynman and Bill Gates: an imaginary encounter. 1999. URL: http://www.trnsoft.com/features/1rfbg.htm
E. M. Rains. Quantum weight enu- merators. IEEE Trans. Inf. Theory, 44(4):1388–1394, 1998.
E. M. Rains. Monotonicity of the quan- tum linear programming bound. IEEE Trans. Inf. Theory, 45(7):2489–2492, 1999.
E. M. Rains. Nonbinary quantum codes. IEEE Trans. Inf. Theory, 45(6):1827– 1832, 1999.
E. M. Rains. Quantum shadow enu- merators. IEEE Trans. Inf. Theory, 45(7):2361–2366, 1999.
M. Roetteler and T. Beth. Polynomial- time solution to the hidden subgroup problem for a class of non-abelian groups. arXive e-print http://www.arXiv.org/abs/quant-ph/9812070, 1998.
A. Ressler. The Design of a Conserva- tive Logic Computer and A Graphical Editor Simulator. Master’s thesis, Mas- sachusetts Institute of Technology, 1981. E. M. Rains, R. H. Hardin, P. W. Shor, and N. J. A. Sloane. Nonadditive quan- tum code. Phys. Rev. Lett., 79(5):953– 954, 1997.
A. Royer. Reduced dynamics with initial correlations, and time-dependent environ- ment and Hamiltonians. Phys. Rev. Lett., 77(16):3272–3275, 1996.
D. W. Robinson and D. Ruelle. Commun. Math. Phys., 5:288, 1967.
R. L. Rivest, A. Shamir, and L. M. Adle- man. A method of obtaining digital sig- natures and public-key cryptosystems. Comm. ACM, 21(2):120–126, 1978.
M. B. Ruskai. Beyond strong subadditiv- ity: improved bounds on the contraction of generalized relative entropy. Rev. Math. Phys., 6(5A):1147–1161, 1994.
S. Ramo, J. R. Whinnery, and T. van Duzer. Fields and waves in communication electronics. Wiley, New York, 1984.
M. Reck, A. Zeilinger, H. J. Bern- stein, and P. Bertani. Experimental real- ization of any discrete unitary operator. Phys. Rev. Lett., 73(1):58–61, 1994.
J. J. Sakurai. Modern Quantum Mechan- ics. Addison-Wesley, Reading, Mass., 1995.
R. Schack and C. M. Caves. Classical model for bulk-ensemble NMR quantum computation. Phys. Rev. A, 60(6):4354– 4362, 1999.
E. Schmidt. Zur theorie der linearen und nichtlinearen integralgleighungen. Math. Annalen., 63:433–476, 1906.
E. Schro ̈ dinger. Probability relations be-
tween separated systems. Proc. Cam- bridge Philos. Soc., 32:446–452, 1936.
B. Schumacher. Quantum coding. Phys. Rev. A, 51:2738–2747, 1995.
B. Schneier. Applied Cryptography. John Wiley and Sons, New York, 1996. B. W. Schumacher. Sending entangle- ment through noisy quantum channels. Phys. Rev. A, 54:2614, 1996.
C. E. Shannon. A mathematical theory of communication. Bell System Tech. J., 27:379–423, 623–656, 1948.
P. W. Shor. Algorithms for quantum com- putation: discrete logarithms and factor- ing. In Proceedings, 35th Annual Sym- posium on Foundations of Computer Science, IEEE Press, Los Alamitos, CA, 1994.
P. Shor. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A, 52:2493, 1995.
P. W. Shor. Fault-tolerant quantum com- putation. In Proceedings, 37th Annual Symposium on Fundamentals of Com- puter Science, pages 56–65, IEEE Press, Los Alamitos, CA, 1996.
P. W. Shor. Polynomial-time algorithms for prime factorization and discrete loga- rithms on a quantum computer. SIAM J. Comp., 26(5):1484–1509, 1997.
B. Simon. Trace Ideals and Their Ap- plications. Cambridge University Press, Cambridge, 1979.
D. Simon. On the power of quantum computation. In Proceedings, 35th An- nual Symposium on Foundations of Computer Science, pages 116–123, IEEE Press, Los Alamitos, CA, 1994.
D. R. Simon. On the power of quan- tum computation. SIAM J. Comput., 26(5):1474–1483, 1997.
P. W. Shor and R. Laflamme. Quantum analog of the MacWilliams identities for classical coding theory. Phys. Rev. Lett., 78(8):1600–1602, 1997.
D. Shasha and C. Lazere. Out of Their Minds: The Lives and Discoveries of 15 Great Computer Scientists. Springer- Verlag, New York, 1998.
D. Slepian, editor. Keys Papers in the Development of Information Theory. IEEE Press, New York, 1974.
C. P. Slichter. Principles of Magnetic Resonance. Springer, Berlin, 1996.
B. W. Schumacher and M. A. Nielsen. Quantum data processing and error cor- rection. Phys. Rev. A, 54(4):2629, 1996. arXive e-print http://www.arXiv.org/abs/quant-ph/9604022.
P. W. Shor and J. Preskill. Simple proof of security of the BB84 quantum key distri- bution protocol. arXive e-print http://www.arXiv.org/abs/quant-ph/0003004, 2000.
R. Solovay and V. Strassen. A fast Monte- Carlo test for primality. SIAM J. Com- put., 6:84–85, 1976.
P. W. Shor and J. A. Smolin. Quan- tum error-correcting codes need not com- pletely reveal the error syndrome. arXive e-print http://www.arXiv.org/abs/quant-ph/9604006, 1996.
A. T. Sornborger and E. D. Stewart. Higher order methods for simulations on quantum computers. Phys. Rev. A, 60(3):1956–1965, 1999. arXive e-print http://www.arXiv.org/abs/quant-ph/9903055.
B. E. A. Saleh and M. C. Teich. Funda- mentals of Photonics. Wiley, NY, 1991. A. M. Steane. Error correcting codes in quantum theory. Phys. Rev. Lett., 77:793, 1996.
A. M. Steane. Multiple particle interfer- ence and quantum error correction. Proc. R. Soc. London A, 452:2551–76, 1996. A. Steane. The ion-trap quantum information processor. Appl. Phys. B – Lasers and Optics, 64(6):623–642, 1997.
A. M. Steane. Efficient fault-tolerant quantum computing. Nature, 399:124– 126, May 1999.
S. Somaroo, C. H. Tseng, T. F. Havel, R. Laflamme, and D. G. Cory. Quan- tum simulations on a quantum computer. Phys. Rev. Lett., 82:5381–5384, 1999. G. Strang. Linear Algebra and Its Ap- plications. Academic Press, New York, 1976.
L. J. Schulman and U. Vazirani. Molec- ular scale heat engines and scalable quan- tum computation. Proc. 31st Ann. ACM Symp. on Theory of Computing (STOC ’99), pages 322–329, 1999.
C. E. Shannon and W. Weaver. The Mathematical Theory of Communica- tion. University of Illinois Press, Urbana, 1949.
N. J. A. Sloane and A. D. Wyner, editors.
Claude Elwood Shannon: Collected Pa- pers. IEEE Press, New York, 1993.
B. Schumacher and M. D. Westmore- land. Sending classical information via
noisy quantum channels. Phys. Rev. A, 56(1):131–138, 1997.
B. Schumacher and M. D. Westmore- land. Quantum privacy and quantum co- herence. Phys. Rev. Lett., 80(25):5695– 5697, 1998.
B. W. Schumacher, M. Westmoreland, and W. K. Wootters. Limitation on the amount of accessible information in a quantum channel. Phys. Rev. Lett., 76:3453, 1996.
L. Szilard. Uber die entropievermin- derung in einen thermodynamischen sys- tem bei eingriffen intelligenter wesen. Z. Phys., 53:840–856, 1929.
B. M. Terhal and D. P. DiVincenzo. The problem of equilibration and the compu- tation of correlation functions on a quan- tum computer. arXive e-print http://www.arXiv.org/abs/quant-ph/9810063, 1998.
Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble. Mea- surement of conditional phase shifts for quantum logic. Phys. Rev. Lett., 75:4710, 1995.
H. F. Trotter. On the product of semi- groups of operators. Proc. Am. Math. Soc., 10:545–551, 1959.
B. S. Tsirelson. Quantum generalizations of Bell’s inequality. Lett. Math. Phys., 4:93, 1980.
A. M. Turing. On computable num- bers, with an application to the Entschei- dungsproblem. Proc. Lond. Math. Soc. 2 (reprinted in [Dav65]), 42:230, 1936. Q. A. Turchette. Quantum optics with single atoms and single photons. Ph.D. thesis, California Institute of Technology, Pasadena, California, 1997.
A. Uhlmann. On the Shannon entropy and related functionals on convex sets. Rep. Math. Phys., 1(2):147–159, 1970. A. Uhlmann. Sa ̈tze u ̈ber dichtematrizen. Wiss. Z. Karl-Marx-Univ. Leipzig, 20:633–637, 1971.
A. Uhlmann. Endlich-dimensionale dichtematrizen I. Wiss. Z. Karl-Marx- Univ. Leipzig, 21:421–452, 1972.
A. Uhlmann. Endlich-dimensionale dichtematrizen II. Wiss. Z. Karl-Marx- Univ. Leipzig, 22:139–177, 1973.
A. Uhlmann. The ‘transition probability’ in the state space of a ∗-algebra. Rep. Math. Phys., 9:273–279, 1976.
A. Uhlmann. Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory. Commun. Math. Phys., 54:21–32, 1977.
H. Umegaki. Ko ̈dai Math. Sem. Rep., 14:59–85, 1962.
L. Vaidman. Teleportation of quantum states. Phys. Rev. A, 49(2):1473–6, 1994. W. van Dam. Quantum oracle interro- gation: getting all information for half the price. In Proceedings of the 39th FOCS, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9805006.
S. J. van Enk. No-cloning and superlu- minal signaling. arXive e-print http://www.arXiv.org/abs/quant-ph/9803030, 1998.
V. Vedral. Landauer’s erasure, error cor- rection and entanglement. arXive e- print http://www.arXiv.org/abs/quant-ph/9903049, 1999.
G. Vidal. Entanglement monotones. arXive e-print http://www.arXiv.org/abs/quant-ph/9807077, 1998.
G. Vidal. Entanglement of pure states for a single copy. Phys. Rev. Lett., 83(5):1046–1049, 1999.
J. von Neumann. Go ̈ ttinger Nachrichten, page 245, 1927.
J. von Neumann. Probabilistic logics and the synthesis of reliable organisms from unreliable components. In Automata Studies, pages 329–378, Princeton Uni- versity Press, Princeton, NJ, 1956.
J. von Neumann. Fourth University of Illinois lecture. In A. W. Burks, editor, Theory of Self-Reproducing Automata, page 66, University of Illinois Press, Ur- bana, 1966.
V. Vedral and M. B. Plenio. Entangle- ment measures and purification proce- dures. Phys. Rev. A, 57(3):1619–1633, 1998.
K. Vogel and H. Risken. Determination of quasiprobability distributions in terms of probability distributions for the ro- tated quadrature phase. Phys. Rev. A, 40(5):2847–2849, 1989.
L. M. K. Vandersypen, C. S. Yannoni, M. H. Sherwood, and I. L. Chuang. Realization of effective pure states for bulk quantum computation. Phys. Rev. Lett., 83:3085–3088, 1999.
R. Vrijen, E. Yablonovitch, K. Wang, H. W. Jiang, A. Balandin, V. Roychowd- hury, T. Mor, and D. DiVincenzo. Elec- tron spin resonance transistors for quan- tum computing in silicon-germanium heterostructures. arXive e-print http://www.arXiv.org/abs/quant-ph/9905096, 1999.
W. Warren. The usefulness of NMR quantum computing. Science, 277(5332):1688, 1997.
J. Watrous. PSPACE has 2-round quan- tum interactive proof systems. arXive e- print cs/9901015, 1999.
S. Winograd and J. D. Cowan. Reliable Computation in the Presence of Noise. MIT Press, Cambridge, MA, 1967.
A. Wehrl. General properties of entropy. Rev. Mod. Phys., 50:221, 1978.
D. J. A. Welsh. Codes and Cryptogra- phy. Oxford University Press, New York, 1988.
S. Wiesner. Unpublished manuscript, circa 1969, appeared as [Wie83].
S. Wiesner. Conjugate coding. SIGACT News, 15:77, 1983.
S. Wiesner. Simulations of many- body quantum systems by a quantum computer. arXive e-print http://www.arXiv.org/abs/quant-ph/9603028, 1996.
D. Williams. Probability with Martin- gales. Cambridge University Press, Cam- bridge, 1991.
E. Winfree. Algorithmic Self-Assembly of DNA. Ph.D. thesis, California Insti- tute of Technology, Pasadena, California, 1998.
D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl. Inst. Stand. Tech., 103:259, 1998.
M. D. Westmoreland and B. Schumacher. Quantum entanglement and the non- existence of superluminal signals. arXive e-print http://www.arXiv.org/abs/quant-ph/9801014, 1998.
E. P. Wigner and M. M. Yanase. Proc. Natl. Acad. Sci. (U S.A.), 49:910–918, 1963.
K. Watanabe and Y. Yamamoto. Limits on tradeoffs between third-order optical nonlinearity, absorption loss, and pulse duration in self-induced transparency and real excitation. Phys. Rev. A, 42(3):1699– 702, 1990.
W. K. Wootters and W. H. Zurek. A sin- gle quantum cannot be cloned. Nature, 299:802–803, 1982.
A. C. Yao. Quantum circuit complexity. Proc. of the 34th Ann. IEEE Symp. on
664
Foundations of Computer Science, pages 352–361, 1993.
S. Younis and T. Knight. Non dissipative rail drivers for adiabatic circuits. In Proceedings, Sixteenth Conference on Ad- vanced Research in VLSI 1995, pages 404–14, IEEE Computer Society Press, Los Alamitos, CA, 1995.
Y. Yamamoto, M. Kitagawa, and K. Igeta. In Proc. 3rd Asia-Pacific Phys. Conf., World Scientific, Singapore, 1988.
H. P. Yuen and M. Ozawa. Ultimate in- formation carrying limit of quantum sys- tems. Physical Review Letters, 70:363– 366, 1993.
F. Yamaguchi and Y. Yamamoto. Crystal lattice quantum computer. Appl. Phys. A, pages 1–8, 1999.
C. Zalka. Simulating quantum systems on a quantum computer. Proc. R. Soc. Lon- don A, 454(1969):313–322, 1998.
C. Zalka. Grover’s quantum searching algorithm is optimal. Phys. Rev. A, 60(4):2746–2751, 1999.
P. Zanardi. Stabilizing quantum informa- tion. arXive e-print http://www.arXiv.org/abs/quant-ph/9910016, 1999.
P. Zoller and C. W. Gardiner. Quantum noise in quantum optics: the stochas- tic Schro ̈ dinger equation. In S. Reynaud, E. Giacobino, and J. Zinn-Justin, editors, Quantum Fluctuations: Les Houches Summer School LXIII, Elsevier, Amsterdam, 1997.
K. Zyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein. Volume of the set of separable states. Phys. Rev. A, 58(2):883– 892, 1999.
W. H. Zurek and R. Laflamme. Quan- tum logical operations on encoded qubits. Phys. Rev. Lett., 77(22):4683–4686, 1996.
X. Zhou, D. W. Leung, and I. L. Chuang. Quantum logic gate constructions with one-bit ”teleportation”. arXive e-print http://www.arXiv.org/abs/quant-ph/0002039, 2000.
P. Zanardi and M. Rasetti. Noise- less quantum codes. Phys. Rev. Lett., 79(17):3306–3309, 1998.
W. H. Zurek. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature, 341:119, 1989.
W. H. Zurek. Decoherence and the transition from quantum to classical. Phys. Today, October 1991.
1-3 ref.
Bibliography
D. Aharonov and M. Ben-Or. Fault tolerant computation with constant error. In Pro- ceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, pp. 176–188, 1997.
A. Abragam. Principles of Nuclear Magnetism. Clarendon Press, Oxford, 1961.
A.G. Anderson, R.L. Garwin, E.L. Hahn, J.W. Horton, G.L. Tucker, and R.M. Walker. J.
Appl. Physics, 26, 1324, 1955.
A. Aspect, P. Grangier, and G. Roger. Experimental tests of realistic local theories via
Bell’s theorem. Phys. Rev. Lett., 47(7), 460–463, 1981.
D. S. Abrams and S. Lloyd. Simulation of many-body Fermi systems on a quantum com-
puter. Phys. Rev. Lett., 79(13), 2586–2589, 1997.
D.S. Abrams and S. Lloyd. Quantum algorithm for providing exponential speed increase
for finding eigenvalues and eigenvectors. Phys. Rev. Lett., 83(24), 5162–5165, 1999.
D. Abramovich and S. Vega. Derivation of broadband and narrowband excitation pulses
using the Floquet formalism. J. Magn. Reson. A, 105(18), 30–48, 1993.
D.V. Averin. Quantum computing and quantum measurement with mesoscopic Josephson
junctions. Fortschr. Phys., 48(9–11), 1055–1074, 2000.
C. H. Bennett and G. Brassard. Quantum cryptography: Public key distribution and coin tossing. In Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, pp. 175–179, IEEE, New York, 1984. Bangalore, India, December 1984.
C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani. Strengths and weaknesses of quantum computing. SIAM J. Comput., 26(5), 1510–1523, 1997.
C. H. Bennett, G. Brassard, C. Cre ́peau, R. Jozsa, A. Peres, and W. Wootters. Teleporting an unknown quantum state via dual classical and EPR channels. Phys. Rev. Lett., 70, 1895, 1993.
A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter. Elementary gates for quantum computation. Phys. Rev. A, 52, 3457–3467, 1995.
M. Boyer, G. Brassard, P. Høyer, and A. Tapp. Tight bounds on quantum searching. Fortsch. Phys. – Prog. Phys., 46(4–5), 493–505, 1998.
D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu. Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolski-Rosen channels. Phys. Rev. Lett., 80, 1121, 1998.
D. Beckman, A. N. Chari, S. Devabhaktuni, and J. Preskill. Efficient networks for quantum factoring. Phys. Rev. A, 54(2), 1034, 1996.
J. Burdon, P.L. Coe, I.B. Haslock, and R.L. Powell. The hydrofluorocarbon 1,1,1,2- tetrafluoroethane (hfc-134a) as a ready source of trifluorovinyllithium. J. Chem. Soc. Chem Commun., pp. 49–50, 1996.
S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack. Separabil- ity of very noisy mixed states and implications for NMR quantum computing. Phys. Rev. Lett., 83(5), 1054–1057, 1999.
G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch. Quantum logic gates in optical lattices. Physical Review Letters, 82, 1060–1063, 1999.
C. H. Bennett and D. P. DiVincenzo. Quantum information and computation. Nature, 404, 247–55, 2000.
J. S. Bell. On the Einstein-Podolsy-Rosen paradox. Physics, 1, 195–200, 1964.
C. H. Bennett. Logical reversibility of computation. IBM J. Res. Dev., 17(6), 525–32,
1973.
P. Benioff. The computer as a physical system: A microscopic quantum mechanical Hamil- tonian model of computers as represented by Turing machines. J. Stat. Phys., 22(5), 563– 591, 1980.
C. H. Bennett. Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett., 68(21), 3121–3124, 1992.
M.V. Berry. Proc. R. Soc. London A, 392, 45, 1984.
C.J. Bauer, R. Freeman, T. Frenkiel, J. Keeler, and A.J. Shaka. Gaussian pulses. J. Magn.
Reson., 58, 442–457, 1984.
J. C. Bergquist, R. G. Hulet, W. M. Itano, and D. J. Wineland. Observation of quantum
jumps in a single atom. Phys. Rev. Lett., 57(14), 1699–1702, 1986.
W. T. Buttler, R. J. Hughes, S. K. Lamoreaux, G. L. Morgan, J. E. Nordholt, and C. G. Peterson. Daylight quantum key distribution over 1.6 km. Phys. Rev. Lett., 84(24), 5652– 5655, 2000.
G. Brassard, P. Høyer, and A. Tapp. Quantum counting. In Automata, Languages and Pro- gramming, 25th Int. Colloquium, Aalborg, Denmark, pp. 13–17, Springer-Verlag, Berlin, 1998. arXive e-print http://www.arXiv.org/abs/quant-ph/9805082.
S.L. Braunstein and H. J. Kimble. Teleportation of continuous quantum variables. Phys. Rev. Lett., 80, 869–872, 1998.
S. Braunstein and H.-K. Lo, editors. Scalable Quantum Computers - paving the way to realization. Wiley, Berlin, Germany, 2000. Reprint of Fortschr. Phys., vol. 48(9-11), 2000. Special issue on the implementation of quantum computers.
F. Bloch. Nuclear induction. Phys. Rev., 70(7-8), 460–474, 1946. N. Bloembergen. Physica, 15, 386, 1949.
R. Bru ̈schweiler, J.C. Madsen, C. Griesinger, O.W. Sørensen, and R.R. Ernst. J. Magn. Reson., 73, 380, 1987.
D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger. Experi- mental quantum teleportation. Nature, 390(6660), 575–579, 1997.
F. Bloch and A. Siegert. Magnetic resonance for nonrotating fields. Phys. Rev., 57, 522– 527, 1940.
M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J.-M. Raimond, and S. Haroche. Quantum rabi oscillation: a direct test of field quantization in a cavity. Phys. Rev. Lett., 76, 1800–1803, 1996.
C. H. Bennett and S. J. Wiesner. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett., 69, 2881–2884, 1992.
R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca. Quantum algorithms revisited. Proc. R. Soc. London A, 454(1969), 339–354, 1998.
D. G. Cory, A. F. Fahmy, and T. F. Havel. Ensemble quantum computing by NMR spec- troscopy. Proc. Nat. Acad. Sci. USA, 94, 1634–1639, 1997.
I. L. Chuang, N. Gershenfeld, and M. Kubinec. Experimental implementation of fast quantum searching. Phys. Rev. Lett., 18(15), 3408–3411, 1998.
I. L. Chuang, N. Gershenfeld, M. G. Kubinec, and D. W. Leung. Bulk quantum compu- tation with nuclear-magnetic-resonance: theory and experiment. Proc. R. Soc. London A, 454(1969), 447–467, 1998.
A. Church. An unsolvable problem of elementary number theory. Am. J. Math., 58, 345, 1936.
D. Collins, K.W. Kim, W.C. Holton, H. Sierzputowska-Gracz, and E.O. Stejskal. NMR quantum computation with indirectly coupled gates. Phys. Rev. A, 62, 022304, 2000.
I. L. Chuang and R. Laflamme. Quantum error correction by coding. arXive e-print http://www.arXiv.org/abs/quant-ph/9511003, Oct 1995.
R. Cleve. The query complexity of order-finding. In Proceedings of the 15th Annual IEEE Conference on Computational Complexity, Firenze, Italy, pp. 54–59, IEEE Computer Society Press, Los Alamitos, CA, 2000. arXive e-print http://www.arXiv.org/abs/quant-ph/9911124.
D.G. Cory, R. Laflamme, E. Knill, L. Viola, T.F. Havel, N. Boulant, G. Boutis, E. Fortu- nato, S. Lloyd, R. Martinez, C. Negrevergne, M. Pravia, Y. Sharf, G. Teklemariam, Y.S. Weinstein, and W.H. Zurek. NMR based quantum information processing: achievements and prospects. Fortschr. Phys., 48(9–11), 875–907, 2000.
D. G. Cory, W. Mass, M. Price, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo. Experimental quantum error correction. Phys. Rev. Lett., 81(10), 2152–2155, 1998.
D. Coppersmith. An approximate Fourier transform useful in quantum factoring. IBM Research Report RC 19642, 1994.
D. G. Cory, M. D. Price, and T. F. Havel. Nuclear magnetic resonance spectroscopy: An experimentally accessible paradigm for quantum computing. Physica D, 120, 82–101, 1998.
T. M. Cover and J. A. Thomas. Elements of Information Theory. John Wiley and Sons, New York, 1991.
C. Cohen-Tannoudji, B. Diu, and F. Laloe ̈. Quantum Mechanics (2 volumes). John Wiley and Sons, New York, 1977.
D.E. Chang, L.M.K. Vandersypen, and M. Steffen. NMR implementation of a building block for scalable quantum computation. Chem. Phys. Lett., 338, 337–344, 2001.
I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd. Experimental realization of a quantum algorithm. Nature, 393(6681), 143–146, 1998.
B.E. Cole, J.B. Williams, B.T. King, M.S. Sherwin, and C.R. Stanley. Coherent manipu- lation of semiconductor quantum bits with terahertz radiation. Nature, 410, 60–63, 2001.
J. I. Cirac and P. Zoller. Quantum computations with cold trapped ions. Phys. Rev. Lett., 74, 4091, 1995.
J. I. Cirac and P. Zoller. A scalable quantum computer with ions in an array of microtraps. Nature, 404, 579–581, 2000.
K. Dorai, Arvind, and A. Kumar. Implementing quantum-logic operations, pseudopure states, and the Deutsch-Jozsa algorithm using non-commuting selective pulses in NMR. Phys. Rev. A, 61, 042306(7), 2000.
M. D. Davis. The Undecidable. Raven Press, Hewlett, New York, 1965.
I.H. Deutsch and G.K. Brennen. Quantum computing with neutral atoms in an optical
lattice. Fortschr. Phys., 48(9-11), 925–943, 2000.
D. Deutsch, A. Barenco, and A. Ekert. Universality in quantum computation. Proc. R.
Soc. London A, 449(1937), 669–677, 1995.
F. Diedrich, J.C. Bergquist, W.M. Itano, and D.J. Wineland. Laser cooling to the zero-point
energy of motion. Phys. Rev. Lett., 62, 430, 1989.
D.P. DiVincenzo, D.P. Bacon, D.A. Lidar, and K.B. Whaley. Universal quantum computa-
tion with the exchange interaction. Nature, 408, 339, 2000.
D. Deutsch. Quantum theory, the Church-Turing Principle and the universal quantum
computer. Proc. R. Soc. Lond. A, 400, 97–117, 1985.
D. Deutsch. Quantum computational networks. Proc. R. Soc. London A, 425, 73, 1989.
D. Dieks. Communication by EPR devices. Phys. Lett. A, 92(6), 271–272, 1982. D. P. DiVincenzo. Quantum computation. Science, 270, 255, 1995.
D. P. DiVincenzo. Two-bit gates are universal for quantum computation. Phys. Rev. A, 51(2), 1015–1022, 1995.
D. P. DiVincenzo. Quantum gates and circuits. Proc. R. Soc. London A, 454, 261–276, 1998.
D. P. DiVincenzo. The physical implementation of quantum computers. Fortschr. Physik, 48(9-11), 771–783, 2000.
D. Deutsch and R. Jozsa. Rapid solution of problems by quantum computation. Proc. R. Soc. London A, 439, 553, 1992.
D.P. DiVincenzo and D. Loss. Quantum computers and quantum coherence. J. Magnetism and Magnetic Matls., 200, 202, 1999.
M. Van der Puy. The reaction of molybdenum hexafluoride with carboxylic acids. J. Fluor. Chem., 13, 375–378, 1979.
L. Emsley and G. Bodenhausen. Phase shifts induced by transient bloch-siegert effects in NMR. Chem. Phys. Lett., 168(3,4), 297–303, 1990.
R. R. Ernst, G. Bodenhausen, and A. Wokaun. Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Oxford University Press, Oxford, 1987.
A. Ekert and R. Jozsa. Quantum computation and Shor’s factoring algorithm. Rev. Mod. Phys., 68, 1, 1996.
J.W. Emsley and J.C. Lindon. NMR Spectroscopy using liquid crystal solvents. Pergamon Press, Oxford, 1975.
D.D. Elleman and S.L. Manatt. J. Chem. Phys., 36, 1945–1947, 1962.
A. Ekert and C. Macchiavello. Error correction in quantum communication. Phys. Rev.
Lett., 77, 2585, 1996.
A. Einstein, B. Podolsky, and N. Rosen. Can quantum-mechanical description of physical
reality be considered complete? Phys. Rev., 47, 777–780, 1935.
R.P. Feynman. There’s plenty of room at the bottom. In Engineer- ing and Science, Caltech, Pasadena, CA, February 1960. Available at http://www.zyvex.com/nanotech/feynman.html.
R. P. Feynman. Simulating physics with computers. Int. J. Theor. Phys., 21, 467, 1982. R. P. Feynman. Quantum mechanical computers. Optics News, p. 11, February 1985. R. P. Feynman. Feynman Lectures on Computation. Addison-Wesley, New York, 1996.
G. Feher and E.A. Gere. Electron spin resonance experiments on donors in silicon. ii. electron spin relaxation effects. Phys. Rev., 114, 1245–1256, 1959.
R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L.W. Molenkamp. Injection and detection of a spin-polarized current in a light emitting diode. Nature, 402, 787–790, 1999.
R. P. Feynman, R. B. Leighton, and M. Sands. Volume III of The Feynman Lectures on Physics. Addison-Wesley, Reading, Mass., 1965.
J.R. Friedman, V. Patel, W. Chen, S.K. Tolpygo, and J.E. Lukens. Quantum superposition of distinct macroscopic states. Nature, 406, 43–46, 2000.
R. Freeman. Spin Choreography. Spektrum, Oxford, 1997.
R. Freeman. Shaped radiofrequency pulses in high resolution NMR. Progr. in NMR
Spectr., 32, 59–106, 1998.
R.J. Fitzgerald, K.L. Sauer, and W. Happer. Chem. Phys. Lett., 284, 87, 1998.
E. Fredkin and T. Toffoli. Conservative logic. Int. J. Theor. Phys., 21(3/4), 219–253, 1982.
X. Fang, X. Zhu, M. Feng, X. Mao, and F. Du. Experimental implementation of dense coding using nuclear magnetic resonance. Phys. Rev. A, 61, 022307(5), 2000.
N. Gershenfeld and I. L. Chuang. Bulk spin resonance quantum computation. Science, 275, 350–356, 1997.
N. Gershenfeld and I.L. Chuang. Quantum computing with molecules. Scientific Ameri- can, June 1998.
D. Gottesman and I. L. Chuang. Quantum teleportation is a universal computational prim- itive. Nature, 402, 390–392, 1999.
H. Geen and R. Freeman. Band-selective radiofrequency pulses. J. Magn. Reson., 93, 93–141, 1991.
J.-M. Gerard and B. Gayral. In H. Benisty, J.-M. Gerard, and C. Weisbuch, editors, QED phenomena and applications of microcavities and photonic crystals, Springer-Verlag, Berlin, 1999.
M. Green, N. Mayne, and F.G.A. Stone. J. Chem. Soc. (A), p. 902, 1968.
D. Gottesman. Theory of fault-tolerant quantum computation. Phys. Rev. A, 57(1), 127–
137, 1998.
L. K. Grover. A fast quantum mechanical algorithm for database search. In 28th ACM Symposium on Theory of Computation, p. 212, Association for Computing Machinery, New York, 1996.
L. K. Grover. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett., 79(2), 325, 1997.
N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden. Quantum cryptography. arXive e-print http://www.arXiv.org/abs/quant-ph/0101098, 2001.
B. Georgeot and D.L. Shepelyanky. Exponential gain in quantum computing of quantum chaos and localization. Phys. Rev. Lett., 86(13), 2890–2893, 2001.
P. Hu ̈bler, J. Bargon, and S.J. Glaser. Nuclear magnetic resonance quantum computing exploiting the pure spin state of para hydrogen. J. Chem. Phys., 113(6), 2056–2059, 2000.
S. E. Hamann, D. L. Haycock, G. Klose, P. H. Pax, I. H. Deutsch, and P. S. Jessen. Resolved-sideband raman cooling to the ground state of an optical lattice. Phys. Rev. Lett., 80, 4149–4152, 1998.
X. Hao, J.S. Moodera, and R. Meservey. Spin-filter effect of ferromagnetic europium sulfide tunnel barriers. Phys. Rev. B, 42(13), 8235–8243, 1990.
D.I. Hoult and R.E. Richards. The signal-to-noise ratio of the nuclear magnetic resonance experiment. J. Magn. Reson., 24, 71–85, 1976.
J.E. Hopcroft and J.D. Ullman. Introduction to automata theory, languages, and compu- tation. Addison-Wesley, Reading, MA, 1979.
G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers, Fourth Edition. Oxford University Press, London, 1960.
A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small. Quantum information processing using quantum dot spins and cavity QED. Phys. Rev. Lett., 83(20), 4204, 1999.
J. Jeener. Superoperators in magnetic resonance. Adv. Magn. Res., 10, 1–51, 1982. C.D. Jeffries. Dynamic nuclear orientation. Wiley, New York, 1963.
J. A. Jones and E. Knill. Efficient refocussing of one spin and two spin interactions for NMR quantum computation. J. Magn. Reson., 141, 322, 1999.
W.R. Dolbier Jr., H. Koroniak, D.J. Burton, P.L. Heinze, A.R. Bailey, G.S. Shaw, and S.W. Hansen. Kinetic and thermodynamic studies of the thermal electrocyclic interconversions of perfluorinated dienes an cyclobutenes. J. Am. Chem. Soc., 109, 219–225, 1987.
J. A. Jones and M. Mosca. Implementation of a quantum algorithm to solve Deutsch’s problem on a nuclear magnetic resonance quantum computer. J. Chem. Phys., 109, 1648, 1998.
J.A. Jones and M. Mosca. Approximate quantum counting on an NMR ensemble quantum computer. Phys. Rev. Lett., 83, 1050, 1999.
J. A. Jones, M. Mosca, and R. H. Hansen. Implementation of a quantum search algorithm on a nuclear magnetic resonance quantum computer. Nature, 393(6683), 344, 1998.
J.A. Jones. NMR quantum computation. Progr. NMR Spectr., 38, 325–360, 2001.
J.M. Kikkawa and D.D. Awschalom. Phys. Rev. Lett., 80, 4313, 1998.
B. Kane. A silicon-based nuclear spin quantum computer. Nature, 393, 133–137, 1998.
E. Knill, I. Chuang, and R. Laflamme. Effective pure states for bulk quantum computation. Phys. Rev. A, 57(5), 3348–3363, 1998.
E ̄ . Kupcˇe and R. Freeman. Close encounters between soft pulses. J. Magn. Reson. A, 112, 261–264, 1995.
A. Yu. Kitaev. Quantum measurements and the Abelian stabilizer problem. arXive e-print http://www.arXiv.org/abs/quant-ph/9511026, 1995.
A. Y. Kitaev. Quantum computations: algorithms and error correction. Russ. Math. Surv., 52(6), 1191–1249, 1997.
E. Knill and R. Laflamme. A theory of quantum error correcting codes. Phys. Rev. A, 55(2), 900–911, 1996.
E. Knill and R. Laflamme. On the power of one bit of quantum information. Phys. Rev. Lett., 81, 5672–5675, 1998.
H. Kim, J.-S. Lee, and S. Lee. Implementation of the refined Deutsch-Jozsa algorithm on a three-bit NMR quantum computer. Phys. Rev. A, 62, 022312, 2000.
E. Knill, R. Laflamme, and G. J. Milburn. A scheme for efficient quantum computation with linear optics. Nature, 409, 46–52, 2001.
E. Knill, R. Laflamme, R. Martinez, and C. Negrevergne. Implementation of the five-qubit error correction benchmark. arXiv:quant-ph/0101034, 2001.
E. Knill, R. Laflamme, R. Martinez, and C.-H. Tseng. An algorithmic benchmark for quantum information processing. Nature, 404, 368–370, 2000.
E. Knill, R. Laflamme, and W. H. Zurek. Resilient quantum computation. Science, 279(5349), 342–345, 1998.
D. E. Knuth. Seminumerical Algorithms 3rd Edition, Volume 2 of The Art of Computer Programming. Addison-Wesley, Reading, Massachusetts, 1998.
N. Koblitz. A Course in Number Theory and Cryptography. Springer-Verlag, New York, 1994.
K. Kraus. States, Effects, and Operations: Fundamental Notions of Quantum Theory. Lecture Notes in Physics, Vol. 190. Springer-Verlag, Berlin, 1983.
A. Khitrin, H. Sun, and B.M. Fung. Method of multifrequency excitation for creating pseudopure states for NMR quantum computing. Phys. Rev. A, 63, 020301(4), 2001.
B. E. King, C. S. Wood, C. J. Myatt, Q. A. Turchette, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland. Cooling the collective motion of trapped ions to initialize a quantum register. Phys. Rev. Lett., 81, 1525–1529, 1998.
R. Landauer. Irreversibility and heat generation in the computing process. IBM J. Res. Dev., 5, 183, 1961.
S. Lloyd and S. Braunstein. Quantum computation over continuous variables. Phys. Rev. Lett., 82, 1784–1787, 1999.
N. Linden, H. Barjat, R.J. Carbajo, and R. Freeman. Pulse sequences for NMR quan- tum computers: how to manipulate nuclear spins while freezing the motion of coupled neighbours. Chem. Phys. Lett., 305, 28–34, 1999.
N. Linden, H. Barjat, and R. Freeman. An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer. Chem. Phys. Lett, 296, 61–67, 1998.
C. Livermore, C.H. Crouch, R.M. Westervelt, K.L. Campman, and A.C. Gossard. The Coulomb blockade in coupled quantum dots. Science, 274, 1332–1335, 1996.
D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto. Efficient implementation of coupled logic gates for quantum computation. Phys. Rev. A, 61, 042310(7), 2000.
Daniel Loss and David P. DiVincenzo. Quantum computation with quantum dots. Phys. Rev. A, 57, 120–126, 1998.
Y. Lecerf. Machines de Turing re ́versibles. Comptes Rendus, 257, 2597–2600, 1963.
J. Levy. Universal quantum computation with spin-1/2 pairs and Heisenberg exchange.
arXive e-print http://www.arXiv.org/abs/quant-ph/0101057, 2001.
M.H. Levitt, R. Freeman, and T. Frenkiel. J. Magn. Reson., 47, 328, 1982.
T.D. Ladd, J.R. Goldman, A. Dana, F. Yamaguchi, and Y. Yamamoto. Quantum compu- tation in a one-dimensional crystal lattice with NMR force microscopy. arXive e-print http://www.arXiv.org/abs/quant-ph/0009122, 2000.
C.K. Law and H.J. Kimble. Deterministic generation of a bit-stream of single-photon pulses. J. Mod. Optics, 44, 2067, 1997.
N. Linden, E ̄. Kupcˇe, and R. Freeman. NMR quantum logic gates for homonuclear spin systems. Chem. Phys. Lett, 311, 321–327, 1999.
R. Laflamme, E. Knill, W. H. Zurek, P. Catasti, and S. V. S. Mariappan. NMR GHZ. Phil. Trans. Roy. Soc. Lond. A, 356, 1941–1948, 1998.
S. Lloyd. A potentially realizable quantum computer. Science, 261, 1569, 1993.
S. Lloyd. Almost any quantum logic gate is universal. Phys. Rev. Lett., 75(2), 346–349,
1995.
Seth Lloyd. Quantum-mechanical computers. Scientific American, 273(4), 44, October 1995.
S. Lloyd. Universal quantum simulators. Science, 273, 1073, 1996.
R. Laflamme, C. Miquel, J.-P. Paz, and W. H. Zurek. Perfect quantum error correction
code. Phys. Rev. Lett., 77, 198, 1996.
D. Leung, L. Vandersypen, X. Zhou, M. Sherwood, C. Yannoni, and I. Chuang. Ex- perimental realization of a two-bit phase damping quantum code. Phys. Rev. A, 60(3), 1924–1943, 1999.
M. Marjanska, I.L. Chuang, and M.G. Kubinec. J. Chem. Phys., 112, 5095, 2000. J.F. Maher and D.F. Evans. Proc. Chem. Soc., pp. 208–209, June 1961.
M. Mehring. High resolution NMR in solids. Spring-Verlag, Berlin, 1983.
N. D. Mermin. Is the moon there when nobody looks? Reality and the quantum theory. Physics Today, p. 45, April 1985.
R. Marx, A.F. Fahmy, J.M. Myers, W. Bermel, and S.J. Glaser. Approaching five-bit NMR quantum computing. Phys. Rev. A, 62, 123310–8, 2000.
X.Maˆıtre,E.Hagley,G.Nogues,C.Wunderlich,P.Goy,M.Brune,J.-M.Raimond,and S. Haroche. Quantum memory with a single photon in a cavity. Phys. Rev. Lett., 79, 769–772, 1997.
G. J. Milburn. Quantum optical Fredkin gate. Phys. Rev. Lett., 62(18), 2124–2127, 1989. I. Malajovich, J. M. Kikkawa, D. D. Awschalom, J. J. Berry, and N. Samarth. Coherent
transfer of spin through a semiconductor heterointerface. Phys. Rev. Lett., 84(5), 2000.
C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland. Demonstration
of a fundamental quantum logic gate. Phys. Rev. Lett., 75, 4714, 1995.
J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Waal, and Lloyd S. Josephson
persistent-current qubit. Science, 285, 1036–1039, 1999.
C. Macchiavello, G.M. Palma, and A. Zeilinger, editors. Quantum computation and quan-
tum information theory. World Scientific, Singapore, 2000.
K. Mølmer and A. Sørensen. Multiparticle entanglement of hot trapped ions. Phys. Rev.
Lett., 82, 1835–1838, 1999.
Y. Maklin, G. Scho ̈n, and A. Shnirman. Josephson-junction qubits with controlled cou-
plings. Nature, 398, 305–307, 1999.
H. Mabuchi, Q.A. Turchette, M.S. Chapman, and H.J. Kimble. Real-time detection of individual atoms falling through a high finesse optical cavity. Opt. Lett., 21, 1393–1395, 1996.
A. Muller, H. Zbinden, and N. Gisin. Quantum cryptography over 23 km in installed under-lake telecom fibre. Europhys. Lett., 33, 334–339, 1996.
M.A. Nielsen and I.L. Chuang. Quantum computation and quantum information. Cam- bridge University Press, Cambridge, England, 2000.
R.J. Nelson, D.G. Cory, and S. Lloyd. Experimental demonstration of Greenberger-Horne- Zeilinger correlations using nuclear magnetic resonance. Phys. Rev. A, 61, 022106(5), 2000.
Y. Nakamura, C.D. Chen, and J.S. Tsai. Spectroscopy of energy-level splitting between two macroscopic quantum states of charge coherently superposed by Josephson coupling. Phys. Rev. Lett., 79, 2328–2331, 1997.
M. A. Nielsen, E. Knill, and R. Laflamme. Complete quantum teleportation using nuclear magnetic resonance. Nature, 396(6706), 52–55, 1998.
Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai. Coherent control of macroscopic quantum states in a single-cooper-pair box. Nature, 398, 786–788, 1999.
G. Nogues, A. Rauschenbeutel, S. Osnaghi, M. Brune, J. M. Raimond, and S. Haroche. Seeing a single photon without destroying it. Nature, 400, 239–242, 1999.
W. Nagourney, J. Sandberg, and H. Dehmelt. Shelved optical electron amplifier: observa- tion of quantum jumps. Phys. Rev. Lett., 56(26), 2797–2799, 1986.
J.-M. Ouvrard, B. N. Ouvrard, J. Courtieu, C. L. Mayne, and D. M. Grant. J. Magn. Reson., 93, 225, 1991.
J.L. O’Brien, S.R. Schofield, M.Y. Simmons, R.G. Clark, A.S. Dzurak, N.J. Curson, B.E. Kane, N. S. McAlpine, M.E. Hawley, and G.W. Brown. Towards the fabrication of phos- phorous qubits for a silicon quantum computer. To appear in Phys. Rev. B, 2001.
Y. Ohno, D.K. Young, B. Beschoten, F. Masukura, H. Ohno, and D.D. Awschalom. Electri- cal spin injection in a ferromagnetic semiconductor heterostructure. Nature, 402, 790–792, 1999.
C. M. Papadimitriou. Computational Complexity. Addison-Wesley, Reading, Mas- sachusetts, 1994.
S.L. Patt. Single- and multiple-frequency-shifted laminar pulses. J. Magn. Reson., 96, 94–102, 1991.
P. M. Platzman and M. I. Dykman. Quantum computing with electrons floating on liquid helium. Science, 284, 1967, 1999.
A. Peres. Quantum Theory: Concepts and Methods. Kluwer Academic, Dordrecht, 1993.
J. Pauly, P. Le Roux, and D. Nishimura. Parameter relations for the Shinnar-Le Roux selective excitation pulse design algorithm. IEEE Transactions on medical imaging, 10(1), 53–65, 1991.
P.Grangier, G. Reymond, and N. Schlosser. Implementations of quantum computing using cavity quantum electrodynamics schemes. Fortschr. Phys., 48(9-11), 859–874, 2000.
A.G. Redfield. IBM J. Res. Dev., 1, 19, 1957.
A.G. Redfield. Adv. Magn. Res., 1, 1–32, 1965.
H. Rohde, S. T. Gulde, C. F. Roos, P. A. Barton, D. Leibfried, J. Eschner, F. Schmidt- Kaler, and R. Blatt. Sympathetic ground state cooling and coherent manipulation with two-ion-crystals. J. Opt. B, 3, S34, 2001.
C. F. Roos, D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt. Ex- perimental demonstration of ground state laser cooling with electromagnetically induced transparency. Phys. Rev. Lett., 85(26), 5547–5550, 2000.
A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.-M. Raimond, and S. Haroche. Step-by-step engineered multiparticle entanglement. Science, 288, 2024– 2028, 2000.
R. L. Rivest, A. Shamir, and L. M. Adleman. A method of obtaining digital signatures and public-key cryptosystems. Comm. ACM, 21(2), 120–126, 1978.
D. Rugar, C.S. Yannoni, and J.A. Sidles. Mechanical detection of magnetic resonance. Nature, 360, 563, 1992.
J. J. Sakurai. Modern Quantum Mechanics. Addison-Wesley, Reading, Mass., 1995.
R. Schack and C. M. Caves. Classical model for bulk-ensemble NMR quantum computa-
tion. Phys. Rev. A, 60(6), 4354–4362, 1999.
E. Schro ̈dinger. Die gegenwa ̈rtage Situation in der Quantenmechanik. Die Naturwis-
senschaften, 48, 807–812, 1935.
Y. Sharf, D.G. Cory, S.S. Somaroo, T.F. Havel, E. Knill, and R. Laflamme. A study of quantum error correction by geometric algebra and liquid-state NMR spectroscopy. Molec. Phys., 98(17), 1347–1363, 2000.
A. Saupe, G. Englert, and A. Povh. ACS Adv. in Chem. Ser., 63, 51, 1967.
Y. Sharf, T.F. Havel, and D.G. Cory. Spatially encoded pseudopure states for NMR
quantum-information processing. Phys. Rev. A, 62, 052314(8), 2000.
P. W. Shor. Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings, 35th Annual Symposium on Foundations of Computer Science, pp. 124–134, IEEE Press, Los Alamitos, CA, 1994.
P. W. Shor. Scheme for reducing decoherence in quantum memory. Phys. Rev. A, 52, 2493, 1995.
P. W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comp., 26(5), 1484–1509, 1997.
D. Simon. On the power of quantum computation. In Proceedings, 35th Annual Sympo- sium on Foundations of Computer Science, pp. 116–123, IEEE Press, Los Alamitos, CA, 1994.
D. R. Simon. On the power of quantum computation. SIAM J. Comput., 26(5), 1474–1483, 1997.
C.A. Sackett, D. Kielpinsky, B.E. King, C. Langer, V. Meyer, C.J. Myatt, M. Rowe, Q.A. Turchette, W.M. Itano, D.J. Wineland, and C. Monroe. Experimental entanglement of four particles. Nature, 404, 256–258, 2000.
C. P. Slichter. Principles of Magnetic Resonance. Springer, Berlin, 1996.
B.C. Stipe, H.J. Mamin, C.S. Yannoni, T.D. Stowe, T.W. Kenny, and D. Rugar. Electron spin relaxation induced by a micron-sized ferromagnet. in preparation for submission to Science, 2001.
B. W. Schumacher and M. A. Nielsen. Quantum data processing and error correction. Phys. Rev. A, 54(4), 2629, 1996.
U. Sakaguchi, H. Ozawa, and T. Fukumi. Method for effective pure states with any number of spins. Phys. Rev. A, 61, 042313(5), 1994.
D. Suter, A. Pines, and M. Mehring. Indirect phase detection of NMR spinor transitions. Phys. Rev. Lett., 57, 242–244, 1986.
A. M. Steane. Error correcting codes in quantum theory. Phys. Rev. Lett., 77, 793, 1996. A. Steane. Quantum computing. Rep. Prog. Phys., 61(2), 117–173, 1998.
S. Somaroo, C. H. Tseng, T. F. Havel, R. Laflamme, and D. G. Cory. Quantum simulations on a quantum computer. Phys. Rev. Lett., 82, 5381–5384, 1999.
L. J. Schulman and U. Vazirani. Molecular scale heat engines and scalable quantum com- putation. Proc. 31st Ann. ACM Symp. on Theory of Computing (STOC ’99), pp. 322–329, 1999.
M. Steffen, L.M.K. Vandersypen, and I.L. Chuang. Simultaneous soft pulses applied at nearby frequencies. J. Magn. Reson., 146, 369–374, 2000.
M. Steffen, L.M.K. Vandersypen, and I.L. Chuang. Toward quantum computation: a five- qubit quantum processor. IEEE Micro, 21(2), 24–34, March 2001.
S. Tarucha, D.G. Austing, T. Honda, R.J. van der Hage, and L. P. Kouwenhoven. Phys. Rev. Lett., 77, 3613, 1996.
A. Tapp. unpublished, 1998.
Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble. Measurement of
conditional phase shifts for quantum logic. Phys. Rev. Lett., 75, 4710, 1995.
P.M. Tedrow and R. Meservey. Spin polarization of electrons tunneling from films of Fe,
Co, Ni and Ga. Phys. Rev. B, 7(1), 318–326, 1973.
T. Toffoli. Reversible computing. In W. de Bakker and J. van Leeuwen, editors, Automata,
Languages, and Programming, pp. 632–644. Springer, New York, 1980.
D.H. Tseng, S. Somaroo, Y. Sharf, E. Knill, R. Laflamme, T.F. Havel, and D.G. Cory. Quantum simulation of a three-body-interaction hamiltonian on an NMR quantum com- puter. Phys. Rev. A, 61, 012302(6), 1999.
A. M. Turing. On computable numbers, with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc. 2 (reprinted in [Dav65]), 42, 230, 1936.
Q.A. Turchette, C.S. Wood, B.E. King, C.J. Myatt, D. Leibfried, W.M. Itano, C. Monroe, and D.J. Wineland. Deterministic entanglement of two trapped ions. Phys. Rev. Lett., 81, 3631–3634, 1998.
W. G. Unruh. Maintaining coherence in quantum computers. Phys. Rev. A, 51(2), 992–997, 1995.
A.S. Verhulst, O. Liivak, H.M. Vieth, C.S. Yannoni, and I.L. Chuang. Non-thermal nuclear magnetic resonance quantum computing using hyperpolarized xenon. submitted to Appl. Phys. Lett., 2001.
L.M.K. Vandersypen, M. Steffen, G. Breyta, C.S. Yannoni, R. Cleve, and I. L. Chuang. Experimental realization of an order-finding algorithm with an NMR quantum computer. Phys. Rev. Lett., 85(25), 5452–5455, 2000.
L.M.K. Vandersypen, M. Steffen, G. Breyta, C.S. Yannoni, R. Cleve, and I. L. Chuang. Experimental realization of Shor’s quantum factoring algorithm. in preparation, 2001.
L.M.K. Vandersypen, M. Steffen, M. H. Sherwood, C.S. Yannoni, G. Breyta, and I. L. Chuang. Implementation of a three-quantum-bit search algorithm. Appl. Phys. Lett., 76(5), 646–648, 2000.
C.H. van der Wal, A.C.J. ter Haar, F.K. Wilhelm, R.N. Schouten, C.J.P.M. Harmans, T.P. Orlando, S. Lloyd, and J.E. Mooij. Quantum superposition of macroscopic persistent- current states. Science, 290, 773–777, 2000.
R.L. Vold and R.R. Vold. Nuclear magnetic relaxation in coupled spin systems. Progr. in NMR Spectr., 12, 79–133, 1978.
L.M.K. Vandersypen, C.S. Yannoni, and I.L. Chuang. Liquid state NMR quantum com- puting. In D.M. Grant and R.K. Harris, editors, to appear in The encyclopedia of NMR (supplement). John Wiley and Sons, West Sussex, England, 2001.
L. M. K. Vandersypen, C. S. Yannoni, M. H. Sherwood, and I. L. Chuang. Realization of effective pure states for bulk quantum computation. Phys. Rev. Lett., 83, 3085–3088, 1999.
R. Vrijen, E. Yablonovitch, K. Wang, H. W. Jiang, A. Balandin, V. Roychowdhury, T. Mor, and D. DiVincenzo. Electron spin resonance transistors for quantum computing in silicon- germanium heterostructures. arXive e-print http://www.arXiv.org/abs/quant-ph/9905096, 1999.
W. Warren. Effects of arbitrary laser or NMR pulse shapes on population inversion and coherence. J. Chem. Phys., 81(12), 5437–5448, 1984.
D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl. Inst. Stand. Tech., 103, 259, 1998.
Y.S. Weinstein, M.A. Pravia, E.M. Fortunato, S. Lloyd, and D.G. Cory. Implementation of the quantum Fourier transform. Phys. Rev. Lett., 86(9), 1889–1891, 2001.
W. K. Wootters and W. H. Zurek. A single quantum cannot be cloned. Nature, 299, 802–803, 1982.
A. C. Yao. Quantum circuit complexity. Proc. of the 34th Ann. IEEE Symp. on Foundations of Computer Science, pp. 352–361, 1993.
C.S. Yannoni, M.H. Sherwood, L.M.K. Vandersypen, M.G. Kubinec, D.C. Miller, and I.L. Chuang. Nuclear magnetic resonance quantum computing using liquid crystal solvents. Appl. Phys. Lett., 75(22), 3563–3565, 1999.
F. Yamaguchi and Y. Yamamoto. Crystal lattice quantum computer. Appl. Phys. A, 68, 1–8, 1999.
W. H. Zurek. Environment-induced super-selection rules. Phys. Rev. D, 26(8), 1862–1880, 1982.
W. H. Zurek. Decoherence and the transition from quantum to classical. Phys. Today, 44(10), 36–44, 1991.
一覧
物理記事 上位100
https://qiita.com/kaizen_nagoya/items/66e90fe31fbe3facc6ff
量子(0) 計算機, 量子力学
https://qiita.com/kaizen_nagoya/items/1cd954cb0eed92879fd4
数学関連記事100
https://qiita.com/kaizen_nagoya/items/d8dadb49a6397e854c6d
言語・文学記事 100
https://qiita.com/kaizen_nagoya/items/42d58d5ef7fb53c407d6
医工連携関連記事一覧
https://qiita.com/kaizen_nagoya/items/6ab51c12ba51bc260a82
自動車 記事 100
https://qiita.com/kaizen_nagoya/items/f7f0b9ab36569ad409c5
通信記事100
https://qiita.com/kaizen_nagoya/items/1d67de5e1cd207b05ef7
日本語(0)一欄
https://qiita.com/kaizen_nagoya/items/7498dcfa3a9ba7fd1e68
英語(0) 一覧
https://qiita.com/kaizen_nagoya/items/680e3f5cbf9430486c7d
転職(0)一覧
https://qiita.com/kaizen_nagoya/items/f77520d378d33451d6fe
仮説(0)一覧(目標100現在40)
https://qiita.com/kaizen_nagoya/items/f000506fe1837b3590df
Qiita(0)Qiita関連記事一覧(自分)
https://qiita.com/kaizen_nagoya/items/58db5fbf036b28e9dfa6
鉄道(0)鉄道のシステム考察はてっちゃんがてつだってくれる
https://qiita.com/kaizen_nagoya/items/26bda595f341a27901a0
安全(0)安全工学シンポジウムに向けて: 21
https://qiita.com/kaizen_nagoya/items/c5d78f3def8195cb2409
一覧の一覧( The directory of directories of mine.) Qiita(100)
https://qiita.com/kaizen_nagoya/items/7eb0e006543886138f39
Ethernet 記事一覧 Ethernet(0)
https://qiita.com/kaizen_nagoya/items/88d35e99f74aefc98794
Wireshark 一覧 wireshark(0)、Ethernet(48)
https://qiita.com/kaizen_nagoya/items/fbed841f61875c4731d0
線網(Wi-Fi)空中線(antenna)(0) 記事一覧(118/300目標)
https://qiita.com/kaizen_nagoya/items/5e5464ac2b24bd4cd001
OSEK OS設計の基礎 OSEK(100)
https://qiita.com/kaizen_nagoya/items/7528a22a14242d2d58a3
Error一覧 error(0)
https://qiita.com/kaizen_nagoya/items/48b6cbc8d68eae2c42b8
プログラマによる、プログラマのための、統計(0)と確率のプログラミングとその後
https://qiita.com/kaizen_nagoya/items/6e9897eb641268766909
官公庁・学校・公的団体(NPOを含む)システムの課題、官(0)
https://qiita.com/kaizen_nagoya/items/04ee6eaf7ec13d3af4c3
「はじめての」シリーズ ベクタージャパン
https://qiita.com/kaizen_nagoya/items/2e41634f6e21a3cf74eb
AUTOSAR(0)Qiita記事一覧, OSEK(75)
https://qiita.com/kaizen_nagoya/items/89c07961b59a8754c869
プログラマが知っていると良い「公序良俗」
https://qiita.com/kaizen_nagoya/items/9fe7c0dfac2fbd77a945
LaTeX(0) 一覧
https://qiita.com/kaizen_nagoya/items/e3f7dafacab58c499792
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、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 20240504
最後までおよみいただきありがとう4ざいました。
いいね 💚、フォローをお願いします。
Thank you very much for reading to the last sentence.
Please press the like icon 💚 and follow me for your happy life.