Quantum complexity theory

SIAM Journal on Computing

Volumn 26, Issue 5, 1997, Pages 1411-1473

  Bernstein, Ethan ^a   Vazirani, Umesh ^b  

^a MICROSOFT   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Fourier sampling; Quantum computation; Quantum polynomial time; Quantum Turing machines; Reversibility; Universal quantum Turing machine

Indexed keywords

EID: 5544255325     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539796300921     Document Type: Article

References (50)

1. L. ADLEMAN, J. DEMARRAIS, AND M. HUANG, Quantum computability, SIAM J. Comput., 26 (1997), pp. 1524-1540.
2. S. ARORA, R. IMPAGLIAZZO, AND U. VAZIRANI, On the Role of the Cook-Levin Theorem in Complexity Theory, manuscript, 1993.
3. S. ARORA, C. LUND, R. MOTWANI, M. SUDAN, AND M. SZEGEDY, Proof verification and intractability of approximation problems, in Proc. 33rd Annual IEEE Symposium on Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1992, pp. 14-23.
4. L. BABAI AND S. MORAN, Arthur-Merlin games: A randomized proof system, and a hierarchy of complexity classes, J. Comput. System Sci., 36 (1988), pp. 254-276.
5. A. BARENCO, C. BENNETT, R. CLEVE, D. DIVINCENZO, N. MARGOLUS, P. SHOR, T. SLEATOR, J. SMOLIN, AND H. WEINFURTER, Elementary gates for quantum computation, Phys. Rev. A, 52 (1995), pp. 3457-3467.
6. P. BENIOFF, Quantum Hamiltonian models of Turing machines, J. Statist. Phys., 29 (1982), pp. 515-546.
7. C. H. BENNETT, Logical reversibility of computation, IBM J. Res. Develop., 17 (1973), pp. 525-532.
8. C. H. BENNETT, Time/space tradeoffs for reversible computation, SIAM J. Comput., 18 (1989), pp. 766-776.
9. C. H. BENNETT, E. BERNSTEIN, G. BRASSARD, AND U. VAZIRANI, Strengths and weaknesses of quantum computing, SIAM J. Comput., 26 (1997), pp. 1510-1523.
10. E. BERNSTEIN, Quantum Complexity Theory, Ph.D. dissertation, Univ. of California, Berkeley, May, 1997.
11. E. BERNSTEIN AND U. VAZIRANI, Quantum complexity theory, in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM, New York, 1993, pp. 11-20.
12. A. BERTHIAUME AND G. BRASSARD, The quantum challenge to structural complexity theory, in Proc. 7th IEEE Conference on Structure in Complexity Theory, 1992, pp. 132-137.
13. A. BERTHIAUME AND G. BRASSARD, Oracle quantum computing, J. Modern Optics, 41 (1994), pp. 2521-2535.
14. A. BERTHIAUME, D. DEUTSCH, AND R. JOZSA, The stabilisation of quantum computation, in Proc. Workshop on Physics and Computation, Dallas, TX, IEEE Computer Society Press, Los Alamitos, CA, 1994, p. 60.
15. N. BSHOUTY AND J. JACKSON, Learning DNF over uniform distribution using a quantum example oracle, in Proc. 8th Annual ACM Conference on Computational Learning Theory, ACM, New York, 1995, pp. 118-127.
16. A. R. CALDERBANK AND P. SHOR, Good quantum error correcting codes exist, Phys. Rev. A, 54 (1996), pp. 1098-1106.
17. CIRAC AND ZOLLER, Quantum, computation using trapped cold ions, Phys. Rev. Lett., 74 (1995), pp. 4091-4094.
18. I. CHUANG, R. LAFLAMME, P. SHOR, AND W. ZUREK, Quantum computers, factoring and decoherence, Science, Dec. 8, 1995, pp. 1633-1635.
19. C. COHEN-TANNOUDJI, B. DIU, AND F. LALOE, Quantum Mechanics, Longman Scientific & Technical, Essex, 1977, pp. 108-181.
20. D. DEUTSCH, Quantum theory, the Church-Turing principle and the universal quantum computer, in Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97-117.
21. D. DEUTSCH, Quantum computational networks, in Proc. Roy. Soc. London Ser. A, 425 (1989), pp. 73-90.
22. D. DEUTSCH AND R. JOZSA, Rapid solution of problems by quantum computation, in Proc. Roy. Soc. London Ser. A, 439 (1992), pp. 553-558.
23. D. DIVINCENZO, Two-bit gates are universal for quantum computation, Phys. Rev. A, 51 (1995), pp. 1015-1022.
24. C. DÜRR, M. SANTHA, AND THANH, A decision procedure for unitary linear quantum cellular automata, in Proc. 37th IEEE Symposium on the Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1996, pp. 38-45.
25. R. FEYNMAN, Simulating physics with computers, Internat. J. Theoret. Phys., 21 (1982), pp. 467-488.
26. R. FEYNMAN, Quantum mechanical computers, Found. Phys., 16 (1986), pp. 507-531; Optics News, February 1985.
27. R. FEYNMAN, Quantum mechanical computers, Found. Phys., 16 (1986), pp. 507-531; Optics News, February 1985.
28. E. FREDKIN AND T. TOFFOLI, Conservative Logic, Internat. J. Theoret. Phys., 21 (1982), p. 219.
29. L. GROVER, A fast quantum mechanical algorithm for database search, in Proc. 28th Annual ACM Symposium on Theory of Computing, ACM, New York, 1996, pp. 212-219.
30. R. LANDAUER, Is quantum mechanics useful?, Phil. Trans. R. Soc. A, 353 (1995), pp. 367-376.
31. R. LIPTON, Personal communication, 1994.
32. S. LLOYD, A potentially realizable quantum computer, Science, 261 (1993), pp. 1569-1571.
33. J. MACHTA, Phase Information in Quantum Oracle Computing, Physics Department, University of Massachusetts, Amherst, MA, manuscript, 1996.
34. K. MORITA, A. SHIRASAKI, AND Y. GONO, A 1-tape 2-symbol reversible Turing machine, IEEE Trans. IEICE, E72 (1989), pp. 223-228.
35. J. VON NEUMANN, Various Techniques Used in Connection with Random Digits, Notes by G. E. Forsythe, National Bureau of Standards, Applied Math Series, 12 (1951), pp. 36-38. Reprinted in von Neumann's Collected Works, Vol. 5, A. H. Taub, ed., Pergamon Press, Elmsford, NY, 1963, pp. 768-770.
36. J. VON NEUMANN, Various Techniques Used in Connection with Random Digits, Notes by G. E. Forsythe, National Bureau of Standards, Applied Math Series, 12 (1951), pp. 36-38. Reprinted in von Neumann's Collected Works, Vol. 5, A. H. Taub, ed., Pergamon Press, Elmsford, NY, 1963, pp. 768-770.
37. G. PALMA, K. SUOMINEN, AND A. EKERT, Quantum Computers and Dissipation, Proc. Roy. Soc. London Ser. A, 452 (1996), pp. 567-584.
38. A. SHAMIR, IP=PSPACE, in Proc. 22nd ACM Symposium on the Theory of Computing, ACM, New York, 1990, pp. 11-15.
39. P. SHOR, Algorithms for quantum computation: Discrete log and factoring, in Proc. 35th Annual IEEE Symposium on Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1994, pp. 124-134.
40. P. SHOR, Fault-tolerant quantum computation, in Proc. 37th Annual IEEE Symposium on the Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1996, pp. 56-65.
41. D. SIMON, On the power of quantum computation, in Proc. 35th Annual IEEE Symposium on Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1994, pp. 116-123; SIAM J. Comput., 26 (1997), pp. 1474-1483.
42. D. SIMON, On the power of quantum computation, in Proc. 35th Annual IEEE Symposium on Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1994, pp. 116-123; SIAM J. Comput., 26 (1997), pp. 1474-1483.
43. R. SOLOVAY AND A. YAO, manuscript, 1996.
44. T. TOFFOLI, Bicontinuous extensions of invertible combinatorial functions, Math. Systems Theory, 14 (1981), pp. 13-23.
45. W. UNRUH, Maintaining coherence in quantum computers, Phys. Rev. A, 51 (1995), p. 992.
46. L. VALIANT, Personal communication, 1992.
47. U. VAZIRANI AND V. VAZIRANI, Random polynomial time is equal to semi-random polynomial time, in Proc. 26th Annual IEEE Symposium on Foundations of Computer Science, 1985, pp. 417-428.
48. J. WATROUS, On one dimensional quantum cellular automata, in Proc. 36th Annual IEEE Symposium on Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1995, pp. 528-537.
49. A. YAO, Quantum circuit complexity, in Proc. 34th Annual IEEE Symposium on Foundations of Computer Science, IEEE Press, Piscataway, NJ, 1993, pp. 352-361.
50. D. ZUCKERMAN, Weak Random Sources, Ph.D. dissertation, Univ. of California, Berkeley, 1990.