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Abstract: We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. -- BQP is low for PP, i.e., PP BQP = PP. -- There exists a relativized world where P = BQP and the polynomial-time hierarchy is infinite. -- There exists a relativized world where BQP does not have complete sets. -- There exists a relativized world where P = BQP but P 6= UP " coUP and... (Update)
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BibTeX entry: (Update)
Lance Fortnow and John Rogers. Complexity limitations on quantum computation. Unpublished manuscript, 1997. http://citeseer.ist.psu.edu/article/fortnow97complexity.html More
@inproceedings{ fortnow98complexity,
author = "Lance Fortnow and John D. Rogers",
title = "Complexity Limitations on Quantum Computation",
booktitle = "{IEEE} Conference on Computational Complexity",
pages = "202--209",
year = "1998",
url = "citeseer.ist.psu.edu/article/fortnow97complexity.html" }
Citations (may not include all citations):1911 Introduction to Automata Theory (context) - Hopcroft, Ullman - 1979
229 Theory of Recursive Functions and Effective Computability (context) - Rogers - 1987 ACM
210 A fast quantum mechanical algorithm for database search - Grover - 1996
173 Quantum complexity theory - Bernstein, Vazirani - 1997 ACM DBLP
164 Polynomial-time algorithms for prime factorization and discr.. - Shor - 1997
144 the power of quantum computation - Simon - 1997
102 Strengths and weaknesses of quantum computing - Bennett, Bernstein et al. - 1997 ACM DBLP
94 Complexity measures for public-key cryptosystems (context) - Grollmann, Selman - 1988 ACM DBLP
86 Gapdefinable counting classes - Fenner, Fortnow et al. - 1994
60 Generic oracles and oracle classes (context) - Blum, Impagliazzo - 1987
57 the degree of boolean functions as real polynomial - Nisan, Szegedy - 1994
45 Quantum computation - Berthiaume - 1997 ACM
34 Relativizable and nonrelativizable theorems in the polynomia.. - Vereshchagin - 1994
32 An oracle builder's toolkit - Fenner, Fortnow et al. - 1993
20 Computational complexity of probabilistic complexity classes (context) - Gill - 1977
20 SIAM Journal on Computing (context) - Adleman, DeMarrais et al. - 1997
20 Separability and one-way functions - Fortnow, Rogers - 1994 ACM DBLP
10 Graph isomorphism is low for PP (context) - Kobler, Schoning et al. - 1992 ACM DBLP
9 Determining acceptance possibility for a quantum computation.. - Fenner, Green et al. - 1998
7 Relationships between quantum and classical space-bounded co.. - Watrous - 1998 ACM DBLP
5 PP and the polynomial hierarchy (context) - Beigel - 1994
4 Department of Computer Science TR (context) - Li, counting et al. - 1993
The graph only includes citing articles where the year of publication is known.
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