Quantum Computation Relative to Oracles
The study of the power and limitations of quantum computation remains a major challenge in complexity theory. Key questions revolve around the quantum complexity classes EQP, BQP, NQP and their derivatives. This paper presents new relativized worlds in which (i) co-RP ⊈ NQE, (ii) P = BQP and UP = EXP, (iii) P = EQP and RP = EXP, and (iv) EQP ⊈ ∑ 2 P ⋃ ∏ 2 P . We also show a partial answer to the question of whether Almost-BQP = BQP.
KeywordsBoolean Function Turing Machine Random Oracle Quantum Network Pseudorandom Generator
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- 2.T. Baker, J. Gill, and R. Solovay, Relativizations ofthe P=?NP question, SIAM J. Comput., 4 (1975), 431–442.Google Scholar
- 3.R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf, Quantum lower bounds by polynomials, in Proc. 39th Symposium on Foundations of Computer Science, pp.352–361,1998.Google Scholar
- 5.R. Beigel, H. Buhrman, and L. Fortnow, NP might not be as easy as detecting unique solutions, in Proc. 30th IEEE Symposium on Theory of Computing, pp.203–208,1998.Google Scholar
- 11.G. Brassard and P. Høyer, An exact quantum polynomial-time algorithm for Simon’s problem, in Proc. 5th Israeli Symposium on Theory of Computing and Systems, pp.12–23, 1997.Google Scholar
- 15.S. Fenner, F. Green, S. Homer, and R. Pruim, Determining acceptance probability for a quantum computation is hard for PH, in Proc. 6th Italian Conference on Theoretical Computer Science, World-Scientific, Singapore, pp.241–252, 1998.Google Scholar
- 16.L. Fortnow and J. Rogers, Complexity limitations on quantum computation, in Proc. 13th Conference on Computational Complexity, pp.202–209, 1998.Google Scholar
- 20.J.T. Håstad, Computational Limitations for Small-Depth Circuits, The MIT Press, 1987.Google Scholar
- 21.E. Hemaspaandra, L.A. Hemaspaandra, and M. Zimand, Almost-everywhere superiority for quantum polynomial time. Technical Report TR-CS-99-720, University of Rochester. See also ph-quantl9910033.Google Scholar
- 26.H. Nishimura and M. Ozawa, Computational complexity of uniform quantum circuit families and quantum Turing machines, manuscript, 1999. See also LANL quant-ph/9906095.Google Scholar
- 29.C.H. Papadimitriou, Computational Complexity, Addison-Wesley, 1994.Google Scholar
- 30.D. Simon, On the power of quantum computation, SIAM J. Comput., 26 (1997), 1340–1349.Google Scholar
- 34.T. Yamakami and A.C. Yao, NQPc = co-C=P. Inform. Process. Lett., 71 (1999),63–69.Google Scholar