On the power of quantum computation

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 356, Issue 1743, 1998, Pages 1759-1768

  Vazirani, Umesh ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Hybrid argument; NP; Oracle; Quantum computation

Indexed keywords

EID: 3042948556     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1998.0247     Document Type: Article

References (23)

1. Aharanov, D. & Ben-Or, M. 1996 Fault tolerant quantum computation with constant error. quant-ph/9611025.
2. Arora, S., Lund, C., Motwani, R., Sudan, M. & Szegedy, M. 1992 Proof verification and intractability of approximation problems. Proc. 33rd A. Symp. on Foundations of Computer Science, pp. 14-23.
3. Arora, S., Impagliazzo, R. & Vazirani, U. 1994 On the role of the Cook-Levin theorem in complexity theory. (Escript available at http//ww.cs.berkeley.edu/∼vazirani.)
4. Beals, R., Buhrman, H., Cleve, R., Mosca, M. & de Wolf, R. 1998 Quantum lower bounds by polynomials. quant-ph/9802049.
5. Bennett, C., Bernstein, E., Brassard, G. & Vazirani, U. 1997 Strengths and weaknesses of quantum computation. SIAM Jl Comp. (Special Issue on Quantum Computing, October.)
6. Bernstein, E. & Vazirani, U. 1993 Quantum complexity theory. Proc. of the 25th A. ACM Symp. on Theory of Computing, pp. 11-20.
7. Bernstein, E. & Vazirani, U. 1997 SIAM J. Comp. (Special Issue on Quantum Computing, October.)
8. Blum, M. & Impagliazzo, R. 1987 Generic oracles and oracle classes. In 28th A. Symp. on the Foundations of Computer Science.
9. Boyer, M., Brassard, G., Høyer, P. & Tapp, A. 1996 Tight bounds on quantum searching. Proc. 4th Workshop on Physics and Computation, Boston, 11/1996, pp. 36-43. New England Complex Systems Institute. (Available at InterJournal at http://interjournal.org.)
10. Cook, S. A. 1971 The complexity of theorem-proving procedures. In Proc. 3rd ACM Symp. on Theory of Computing, pp. 151-158.
11. Deutsch, D. 1989 Quantum computational networks. Proc. R. Soc. Lond. A 425, 73-90.
12. Deutsch, D. & Jozsa, R. 1992 Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553-558.
13. Gottesman, D. 1997 A theory of fault-tolerant quantum computation, quant-ph/9702029.
14. Grover, L. 1996 A fast quantum mechanical algorithm for database search. Proc. 28th A. ACM Symp. on Theory of Computing, pp. 212-219.
15. Levin, L. 1973 Universal'nyǐe perebornyǐe zadachi. Problemy Peredachi Informatsii 9, 265-266 (In Russian).
16. Nisan, N. 1989 CREW PRAM's and decision trees. In Proc. 21st ACM Symp. on Theory of Computing, pp. 327-335.
17. Shamir, A. 1979 Factoring numbers in O(logn) arithmetic steps. Informat. Processing Lett. 8(10), 28-31.
18. Shamir, A. 1990 IP = PSPACE. In Proc. 22nd ACM Symp. on Theory of Computing, pp. 11-15.
19. Shor, P. W. 1994 Algorithms for quantum computation: discrete logarithms and factoring. In Proc. 35th A. IEEE Symp. on Foundations of Computer Science, pp. 124-134.
20. Shor, P. W. 1997 SIAM Jl Comp. (Special Issue on Quantum Computing, October.)
21. Simon, D. 1994 On the power of quantum computation. Proc. 35th A. IEEE Symp. on Foundations of Computer Science, pp. 116-123.
22. Simon, D. 1997 SIAM Jl Comp. (Special Issue on Quantum Computing, October.)
23. Vergis, A., Steiglitz, K. & Dickinson, B. 1986 The complexity of analog computation. Math. Computers Simul. 28, 91-113.