On the power of quantum computation

SIAM Journal on Computing

Volumn 26, Issue 5, 1997, Pages 1474-1483

  Simon, Daniel R ^a  

^a MICROSOFT   (United States)

Author keywords

Complexity theory; Oracles; Quantum computation

Indexed keywords

POLYNOMIAL APPROXIMATION; PROBABILITY DISTRIBUTIONS; QUANTUM THEORY; TURING MACHINES;

COMPLEXITY THEORY; DISCRETE LOGARITHMS; FACTORING PROBLEM; ORACLES; POLYNOMIAL-TIME ALGORITHMS; QUANTUM MECHANICAL; QUANTUM MODEL OF COMPUTATION; UNIFORM DISTRIBUTION;

QUANTUM COMPUTERS;

EID: 0009438294     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539796298637     Document Type: Article

References (23)

1. P. BENIOFF, Quantum mechanical Hamiltonian models of Turing machines, J. Statist. Phys., 29 (1982), pp. 515-546.
2. C. H. BENNETT, Logical reversibility of computation, IBM J. Res. Develop., 17 (1973), pp. 525-532.
3. C. H. BENNETT, E. BERNSTEIN, G. BRASSARD, AND U. VAZIRANI, Strengths and weaknesses of quantum computing, SIAM J. Comput., 26 (1997), pp. 1510-1523.
4. A. BERTHIAUME AND G. BRASSARD, The quantum challenge to structural complexity theory, in Proc. 7th IEEE Conference on Structure in Complexity Theory, Boston, MA, 1992, pp. 132-137.
5. A. BERTHIAUME AND G. BRASSARD, Oracle quantum computing, J. Modern Optics, 41 (1994), pp. 2521-2535.
6. 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.
7. E. BERNSTEIN AND U. VAZIRANI, Quantum complexity theory, in Proc. 25th ACM Symp. on Theory of Computation, San Diego, CA, 1993, pp. 11-20; SIAM J. Comput., 26 (1997), pp. 1411-1473.
8. E. BERNSTEIN AND U. VAZIRANI, Quantum complexity theory, in Proc. 25th ACM Symp. on Theory of Computation, San Diego, CA, 1993, pp. 11-20; SIAM J. Comput., 26 (1997), pp. 1411-1473.
9. B. CHOR AND O. GOLDREICH, Unbiased bits from sources of weak randomness and probabilistic communication complexity, SIAM J. Comput., 17 (1988), pp. 230-261.
10. D. DEUTSCH, Quantum theory, the Church-Turing principle and the universal quantum computer, in Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 73-90.
11. D. DEUTSCH, Quantum computational networks, in Proc. Roy. Soc. London Ser. A, 425 (1989), pp. 73-90.
12. D. DIVINCENZO, Two-bit gates are universal for quantum computation, Phys. Rev. A, 51 (1995), pp. 1015-1022.
13. D. DEUTSCH AND R. JOZSA, Rapid solution of problems by quantum computation, in Proc. Roy. Soc. London Ser. A, 439 (1992), pp. 553-558.
14. C. DÜRR, H. LÊ THANK, AND M. SANTHA, A decision procedure for well-formed linear quantum cellular automata, in Proc. 13th Symposium on Theoretical Aspects of Computer Science, Grenoble, France, 1996, pp. 281-292.
15. R. FEYNMAN, Simulating physics with computers, Internat. J. Theoret. Phys., 21 (1982), pp. 467-488.
16. R. FEYNMAN, Quantum mechanical computers, Found. Phys., 16 (1986), pp. 507-531.
17. L. GROVER, A fast quantum mechanical algorithm for database search, in Proc. 28th ACM Symp. on Theory of Computation, Philadelphia, PA, 1996, pp. 212-219.
18. n ou θ est un "isomorphism de codes", Comptes Rendus de L'Academie Francaise des Sciences, 257 (1963), pp. 2597-2600.
19. P. SHOR, Algorithms for quantum computation: Discrete log and factoring, in Proc. 35th IEEE Symp. on Foundations of Computer Science, Santa Fe, NM, 1994, pp. 124-134.
20. P. SHOR, Fault-tolerant quantum computation, in Proc. 37th IEEE Symp. on Foundations of Computer Science, Burlington, VT, 1996, pp. 56-65.
21. D. SIMON, On the power of quantum computation, in Proc. 35th IEEE Symp. on Foundations of Computer Science, Santa Fe, NM, 1994, pp. 116-123.
22. U. V. VAZIRANI AND V. V. VAZIRANI, Random polynomial time is equal to slightly-random polynomial time, in Proc. 26th IEEE Symp. on Foundations of Computer Science, Portland, OR, 1985, pp. 417-428.
23. A. YAO, Quantum circuit complexity, in Proc. 34th IEEE Symp. on Foundations of Computer Science, Palo Alto, CA, 1993, pp. 352-361.