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Abstract: Building on work of Deutsch and Jozsa, we construct oracles relative to which (1) there is a decision problem that can be solved with certainty in worst-case polynomial time on the quantum computer, yet it cannot be solved classically in probabilistic expected polynomial time if errors are not tolerated nor even in nondeterministic polynomial time, and (2) there is a decision problem that can be solved in exponential time on the quantum computer, which requires double exponential time on all... (Update)
Context of citations to this paper: More
...by the the black box, or oracle, model of computation. The algorithms of Deutsch [38] Deutsch Jozsa [39] Berthiaume Brassard [23], Bernstein Vazirani [22] Simon [92] Grover [48] and Buhrman van Dam [28] give examples of problems for which we have a quantum...
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BibTeX entry: (Update)
Berthiaume, A. and G. Brassard. Oracle quantum computing, In Proceedings of the Workshop on Physics and Computation - Physcomp '92, pages 195-199. IEEE Press, (October 1992). http://citeseer.ist.psu.edu/article/berthiaume94oracle.html More
@inproceedings{ berthiaume92oracle,
author = "A.~Berthiaume and Gilles Brassard",
title = "Oracle quantum computing",
booktitle = "Proceedings of the Workshop on Physics of Computation: PhysComp '92",
publisher = "Institute of Electrical and Electronic Engineers Computer Society Press",
address = "Los Alamitos, CA",
pages = "195--199",
year = "1992",
url = "citeseer.ist.psu.edu/article/berthiaume94oracle.html" }
Citations (may not include all citations):773 Reducibility among combinatorial problems (context) - Karp - 1972
534 The complexity of theorem proving procedures (context) - Cook - 1971
175 Logical Reversibility of Computation (context) - Bennett - 1973
173 Quantum Complexity Theory - Bernstein, Vazirani - 1993
145 Computational complexity of probabilistic Turing machines (context) - Gill - 1977
144 the power of quantum computation - Simon - 1993
126 Rapid solution of problems by quantum computation (context) - Deutsch, Jozsa - 1992
116 Simulating physics with computers - Feynman - 1982
94 Complexity measures for public-key cryptosystems (context) - Grollmann, Selman - 1988
86 Gap-definable counting classes - Fenner, Fortnow et al. - 1991
83 A machine independent theory of the complexity of recursive .. (context) - Blum - 1967
67 Experimental quantum cryptography - Bennett, Bessette et al. - 1992
48 Quantum theory, the Church--Turing principle and the univers.. - Deutsch - 1985
42 The quantum challenge to structural complexity theory - Berthiaume, Brassard - 1992
37 A potentially realizable quantum computer (context) - Lloyd - 1993
36 Oracle Quantum Computing - Berthiaume, Brassard - 1992
33 Quantum Cryptography (context) - Bennett, Brassard et al. - 1992
8 Characterizing classes of functions computable by quantum pa.. (context) - Jozsa - 1991
4 Machines de Turing r'eversibles. R'ecursive insolubilit'e en.. (context) - Lecerf - 1963
3 Reducibility, randomness, and intractability (context) - Adleman, Manders - 1977
1 Negative probability (context) - Feynman - 1987
1 Relativizations of the P ? = NP question (context) - Baker, Gill et al. - 1975
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://andre.cs.depaul.edu/andre/publicat.htm): More
The Quantum Challenge to Structural Complexity Theory - Berthiaume, Brassard (1992) (Correct)
The Stabilisation of Quantum Computations - Berthiaume, Deutsch, Jozsa (1994) (Correct)
Oracle Quantum Computing - Berthiaume, Brassard (1992) (Correct)
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