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Abstract: This paper studies fundamental questions in computational learning theory from a quantum computation perspective. We consider quantum versions of two well-studied classical learning models: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples. We give positive and negative results for quantum versus classical learnability. For each of the two learning models described above, we show that any concept... (Update)
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BibTeX entry: (Update)
R. A. Servedio and S. J. Gortler, "Quantum versus classical learnability", in Proceedings of the 16th Annual IEEE Conference on Computational Complexity, Chicago, IL, 18--21 June 2001. http://citeseer.ist.psu.edu/article/servedio00quantum.html More
@inproceedings{ servedio01quantum,
author = "Servedio and Gortler",
title = "Quantum versus Classical Learnability",
booktitle = "{SCT}: Annual Conference on Structure in Complexity Theory",
year = "2001",
url = "citeseer.ist.psu.edu/article/servedio00quantum.html" }
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465 Learnability and the Vapnik-Chervonenkis Dimension (context) - Blumer, Ehrenfeucht et al. - 1989
454 the uniform convergence of relative frequencies of events to.. (context) - Vapnik, Chervonenkis - 1971
441 Queries and concept learning (context) - Angluin - 1988
248 An Introduction to Computational Learning Theory (context) - Kearns, Vazirani - 1994
210 A fast quantum mechanical algorithm for database search - Grover - 1996
184 Cryptographic limitations on learning boolean formulae and n.. - Kearns, Valiant - 1994
173 Quantum complexity theory - Bernstein, Vazirani - 1997
164 Polynomial-time algorithms for prime factorization and discr.. - Shor - 1997
151 A general lower bound on the number of examples needed for l.. (context) - Ehrenfeucht, Haussler et al. - 1989
144 the power of quantum computation - Simon - 1997
126 Rapid solution of problems by quantum computation (context) - Deutsch, Jozsa - 1992
102 Strengths and weaknesses of quantum computing - Bennett, Bernstein et al. - 1997
97 Introduction to Coding Theory (context) - Van Lint - 1992
85 Quantum circuit complexity - Yao - 1993
82 When won't membership queries help (context) - Angluin, Kharitonov - 1995
73 Tight bounds on quantum searching - Boyer, Brassard et al. - 1998
49 Quantum lower bounds by polynomials - Beals, Buhrman et al.
46 An exact quantum polynomial-time algorithm for Simon's probl.. - Brassard, yer - 1997
42 Computational Learning Theory: an Introduction (context) - Anthony, Biggs - 1997
36 How many queries are needed to learn - Hellerstein, Pillaipakkamnatt et al. - 1996
36 Complexity limitations on quantum computation - Fortnow, Rogers - 1998
32 An oracle builder's toolkit - Fenner, Fortnow et al. - 1993
30 Quantum counting - Brassard, yer et al. - 1998
29 classical communication and computation (context) - Buhrman, Cleve et al.
21 Grover's quantum searching algorithm is optimal (context) - Zalka
16 Oracles and queries that are sucient for exact learning (context) - Bshouty, Cleve et al. - 1996
14 Learning DNF over the uniform distribution using a quantum e.. - Bshouty, Jackson - 1999
11 An introduction to quantum complexity theory (context) - Cleve
11 Matrix Theory: a second course (context) - Ortega - 1987
7 The complexity of learning with queries (context) - Gavald - 1994
6 Generalized teaching dimensions and the query complexity of .. (context) - Hegedus
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