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This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers.
On the uniform convergence of relative frequencies of events to their probabilities
V. Vapnik and A. Chervonenkis · 1968
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Bounds for the quantity of information transmitted by a quantum communication channel
A. S. Holevo · 1973
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Theory of pattern recognition
V. Vapnik and A. Chervonenkis · 1974
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Vychislimoe i nevychislimoe (computable and noncomputable)
Y. Manin · 1980
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Quantum mechanical Hamiltonian models of Turing machines
P. A. Benioff · 1982
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Simulating physics with computers
R. Feynman · 1982
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Conditional tests
M. Yu. Moshkov · 1983
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A theory of the learnable
L. Valiant · 1984
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Quantum theory, the Church-Turing principle, and the universal quantum Turing machine
D. Deutsch · 1985
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Quantum mechanical computers
R. Feynman · 1985
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Queries and concept learning
D. Angluin · 1987
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Learnability and the Vapnik-Chervonenkis dimension
A. Blumer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth · 1989
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A hard-core predicate for all one-way functions
O. Goldreich and L. Levin · 1989
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Learning DNF under the uniform distribution in quasi-polynomial time
K. A. Verbeurgt · 1990
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Decision theoretic generalizations of the PAC model for neural net and other learning applications
D. Haussler · 1992
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Constant depth circuits, Fourier transform, and learnability
N. Linial, Y. Mansour, and N. Nisan · 1993
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Toward efficient agnostic learning
M. J. Kearns, R. E. Schapire, and L. Sellie · 1994
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Cryptographic limitations on learning Boolean formulae and finite automata
M. J. Kearns and L. G. Valiant · 1994
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An introduction to computational learning theory
M. J. Kearns and U. V. Vazirani · 1994
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Sharper bounds for Gaussian and empirical processes
M. Talagrand · 1994
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When won’t membership queries help?
D. Angluin and M. Kharitonov · 1995
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Boosting a weak learning algorithm by majority
Y. Freund · 1995
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Generalized teaching dimensions and the query complexity of learning
T. Hegedűs · 1995
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Oracles and queries that are sufficient for exact learning
N. H. Bshouty, R. Cleve, R. Gavaldà, S. Kannan, and C. Tamon · 1996
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A fast quantum mechanical algorithm for database search
L. K. Grover · 1996
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General bounds on the number of examples needed for learning probabilistic concepts
H. U. Simon · 1996
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Strengths and weaknesses of quantum computing
C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani · 1997
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Quantum complexity theory
E. Bernstein and U. Vazirani · 1997
Earlier work this paper cites.
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
J. C. Jackson · 1997
Cited alongside, same era.
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
P. W. Shor · 1997
Cited alongside, same era.
On the power of quantum computation
D. Simon · 1997
Cited alongside, same era.
Prediction, learning, uniform convergence, and scale-sensitive dimensions
P. Bartlett and P. M. Long · 1998
Cited alongside, same era.
Learning DNF over the uniform distribution using a quantum example oracle
N. H. Bshouty and J. C. Jackson · 1999
Cited alongside, same era.
Classical computing, quantum computing, and Shor’s factoring algorithm
Y. Manin · 1999
Cited alongside, same era.
An improved lower bound on query complexity for quantum PAC learning
C. Zhang · 2010
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Quantum predictive learning and communication complexity with single input
D. Gavinsky · 2012
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Quantum computing and learning theory
R. Kothari · 2012
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Quantum speed-up for unsupervised learning
E. Aïmeur, G. Brassard, and S. Gambs · 2013
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Quantum algorithms for supervised and unsupervised machine learning, 1 Jul 2013
S. Lloyd, M. Mohseni, and P. Rebentrost · 2013
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Function learning from interpolation
M. Anthony and P. Bartlett · 2000
Cited alongside, same era.
Quantum Computation and Quantum Information
M. A. Nielsen and I. L. Chuang · 2000
Cited alongside, same era.
Quantum lower bounds by quantum arguments
A. Ambainis · 2002
Cited alongside, same era.
Dense quantum coding and quantum finite automata
A. Ambainis, A. Nayak, A. Ta-Shma, and U. V. Vazirani · 2002
Cited alongside, same era.
Quantum amplitude amplification and estimation
G. Brassard, P. Høyer, M. Mosca, and A. Tapp · 2002
Cited alongside, same era.
Reversing quantum dynamics with near-optimal quantum and classical fidelity
H. Barnum and E. Knill · 2002
Cited alongside, same era.
S. Lloyd, M. Mohseni, and P. Rebentrost · 2013
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Quantum support vector machine for big data classification
P. Rebentrost, M. Mohseni, and S. Lloyd · 2013
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An optimal quantum algorithm for the oracle identification problem
R. Kothari · 2014
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Analysis of Boolean Functions
R. O’Donnell · 2014
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Understanding machine learning: From theory to algorithms
S. Shalev-Shwartz and S. Ben-David · 2014
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Quantum Machine Learning: What Quantum Computing Means to Data Mining
P. Wittek · 2014
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Advances in quantum machine learning, 9 Dec 2015
J. Adcock, E. Allen, M. Day, S. Frick, J. Hinchliff, M. Johnson, S. Morley-Short, S. Pallister, A. Price, and S. Stanisic · 2015
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Quantum machine learning algorithms: Read the fine print
S. Aaronson · 2015
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Quantum algorithms for learning symmetric juntas via the adversary bound
A. Belovs · 2015
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An almost optimal PAC algorithm
H. U. Simon · 2015
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An introduction to quantum machine learning
M. Schuld, I. Sinayskiy, and F. Petruccione · 2015
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Complexity-theoretic foundations of quantum supremacy experiments
S. Aaronson and L. Chen · 2016
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Quantum machine learning, 28 Nov 2016
J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd · 2016
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The learnability of unknown quantum measurements
H. C. Cheng, M. H. Hsieh, and P. C. Yeh · 2016
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Complexity theoretic limitations on learning DNF’s
A. Daniely and S. Shalev-Shwartz · 2016
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The optimal sample complexity of PAC learning
S. Hanneke · 2016
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Sample-optimal tomography of quantum states
J. Haah, A. W. Harrow, Z. Ji, X. Wu, and N. Yi · 2016
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Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb tester
C. Y.-Y. Lin and H. Lin · 2016
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R. O’Donnell and J. Wright · 2016
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N. Wiebe, A. Kapoor, and K. Svore · 2016
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Quantum perceptron models, 2016
N. Wiebe, A. Kapoor, and K. M. Svore · 2016
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Optimal quantum sample complexity of learning algorithms
S. Arunachalam and R. de Wolf · 2017
Closest in time.
Quantum recommendation systems
I. Kerenidis and A. Prakash · 2017
Closest in time.