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Abstract: It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation. This result is achieved by showing that the complexity class NQP of Adleman, Demarrais, and... (Update)
Context of citations to this paper: More
...the QACC operator is non zero. This is analogous to the de nition of the class NQP in Adleman et al. 10] and discussed in Fenner et al. [11] where it is shown that NQP is classically of high complexity, and in particular is hard for the polynomial time hierarchy. In this way...
...lies in the polynomial time hierarchy. What about quantum variations of NP and interactive proof systems Fenner, Green, Homer and Pruim [FGHP99] consider the class consisting of the languages L such that for some polynomialtime quantum Turing machine, x is in L when M(x)...
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BibTeX entry: (Update)
S. Fenner, F. Green, S. Homer, and R. Pruim. Determining acceptance possibility for a quantum computation is hard for PH. Technical Report 98-008, Computer Science Department, Boston University, 1998. http://citeseer.ist.psu.edu/fenner98determining.html More
@article{ fenner99determining,
author = "Stephen A. Fenner and Frederic Green and Steven Homer and Randall Pruim",
title = "Determining Acceptance Possibility for a Quantum Computation is Hard for the Polynomial Hierarchy",
journal = "Electronic Colloquium on Computational Complexity (ECCC)",
volume = "6",
number = "003",
year = "1999",
url = "citeseer.ist.psu.edu/fenner98determining.html" }
Citations (may not include all citations):173 Quantum Complexity Theory - Bernstein, Vazirani - 1997 ACM DBLP
168 Algorithms for quantum computation: Discrete logarithms and .. - Shor - 1994 DBLP
144 the power of quantum computation - Simon - 1997
126 PP is as hard as the polynomial-time hierarchy (context) - Toda - 1991 ACM DBLP
126 Rapid solutions of problems by quantum computation (context) - Deutsch, Jozsa - 1992
90 The complexity of combinatorial problems with succinct input.. (context) - Wagner - 1986 ACM DBLP
86 Gap-definable counting classes - Fenner, Fortnow et al. - 1994 ACM DBLP
85 Quantum circuit complexity - Yao - 1993 DBLP
58 volume 11 of EATCS Monographs on Theoretical Computer Scienc.. (context) - Balc'azar, 'iaz et al. - 1988
53 Counting classes are at least as hard as the polynomial-time.. (context) - Toda, Ogiwara - 1992 ACM DBLP
45 Quantum computation - Berthiaume - 1997 ACM
44 The Graph Isomorphism Problem: Its Structural Complexity (context) - Kobler, Schoning et al. - 1993
42 The quantum challenge to structural complexity theory - Berthiaume, Brassard - 1992 DBLP
37 Complexity classes defined by counting quantifiers - Tor'an - 1991 ACM DBLP
36 Complexity limitations on quantum computation - Fortnow, Rogers - 1998 ACM DBLP
34 Quantum mechanical hamiltonian models of turing machines (context) - Benioff - 1982
20 SIAM Journal on Computing (context) - Adleman, DeMarrais et al. - 1997
18 Counting Complexity - Fortnow - 1997 ACM
14 Polynomial-time algorithms for prime number factorization an.. (context) - Shor - 1997
13 Strengths and weaknesses of quantum computation (context) - Bennett, Bernstein et al. - 1997
13 Theoretical Computer Science (context) - Tarui, AC et al. - 1993 ACM
9 The Power of Counting (context) - Schoning - 1990
9 and the universal quantum computer (context) - Deutsch, the - 1985
7 Quantum NP is Hard for PH - Fenner, Green et al. - 1998
3 Private communication (context) - Watrous - 1997
The graph only includes citing articles where the year of publication is known.
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