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Abstract: This is a non-technical survey paper of recent quantum-mechanical discoveries that challenge generally accepted complexity-theoretic versions of the Church--Turing thesis. In particular, building on pionering work of David Deutsch and Richard Jozsa, we construct an oracle relative to which there exists a set that can be recognized in Quantum Polynomial Time (QP), yet any Turing machine that recognizes it would require exponential time even if allowed to be probabilistic, provided that errors... (Update)
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BibTeX entry: (Update)
Andr`e Berthiaume and Gilles Brassard. The quantum challenge to structural complexity theory. In Proceedings of the 7th IEEE Structure in Complexity Theory Conference, pages 132--137. IEEE, 1992. http://citeseer.ist.psu.edu/berthiaume92quantum.html More
@inproceedings{ berthiaume92quantum,
author = "A.~Berthiaume and Gilles Brassard",
title = "The quantum challenge to structural complexity theory",
booktitle = "Proceedings of the Seventh Annual Structure in Complexity Theory Conference",
publisher = "Institute of Electrical and Electronic Engineers Computer Society Press",
address = "Los Alamitos, CA",
pages = "132--137",
year = "1992",
url = "citeseer.ist.psu.edu/berthiaume92quantum.html" }
Citations (may not include all citations):145 Computational complexity of probabilistic Turing machines (context) - Gill - 1977 ACM DBLP
126 Rapid solution of problems by quantum computation (context) - Deutsch, Jozsa - 1991
95 Limits on the provable consequences of one-way permutations - Impagliazzo, Rudich - 1989
94 Complexity measures for public-key cryptosystems (context) - Grollmann, Selman - 1988
90 Quantum cryptography: Public key distribution and coin tossi.. (context) - Bennett, Brassard - 1984
86 Gapdefinable counting classes - Fenner, Fortnow et al. - 1991
67 Experimental quantum cryptography - Bennett, Bessette et al. ACM DBLP
48 Quantum theory, the Church-- Turing principle and the univer.. - Deutsch - 1985
42 Practical quantum oblivious transfer - Bennett, Brassard et al. - 1991
14 Quantum bit commitment and coin tossing protocols - Brassard, Cr'epeau - 1990 ACM DBLP
14 Quantum cryptography without Bell's theorem (context) - Bennett, Brassard et al. - 1992
8 Characterizing classes of functions computable by quantum pa.. (context) - Jozsa - 1991
1 Reducibility, randomness, and intractibility (context) - Adleman, Manders - 1977
The graph only includes citing articles where the year of publication is known.
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Oracle Quantum Computing - Berthiaume, Brassard (1994) (Correct)
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