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We present several quantum algorithms for performing nearest-neighbor learning.
Nearest neighbor pattern classification
Thomas Cover and Peter Hart · 1967
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Some methods for classification and analysis of multivariate observations, 1967
J. MacQueen · 1967
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A branch and bound algorithm for computing k-nearest neighbors
Keinosuke Fukunaga and Patrenahalli M. Narendra · 1975
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Least squares quantization in PCM
Stuart Lloyd · 1982
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Inductive knowledge acquisition: a case study
John Ross Quinlan, PJ Compton, KA Horn, and L Lazarus · 1987
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Breast cancer diagnosis and prognosis via linear programming
Olvi L Mangasarian, W Nick Street, and William H Wolberg · 1995
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A quantum algorithm for finding the minimum
Christoph Dürr and Peter Høyer · 1996
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The MNIST database of handwritten digits, 1998
Yann LeCun and Corinna Cortes · 1998
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The quantum query complexity of approximating the median and related statistics
Ashwin Nayak and Felix Wu · 1999
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Quantum amplitude amplification and estimation
Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp · 2000
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Quantum fingerprinting
Harry Buhrman, Richard Cleve, John Watrous, and Ronald De Wolf · 2001
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Anti-spam filtering: a centroid-based classification approach
Nuanwan Soonthornphisaj, Kanokwan Chaikulseriwat, and Piyanan Tang-On · 2002
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Creating superpositions that correspond to efficiently integrable probability distributions
Lov Grover and Terry Rudolph · 2002
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Diagnosis of multiple cancer types by shrunken centroids of gene expression
Robert Tibshirani, Trevor Hastie, Balasubramanian Narasimhan, and Gilbert Chu · 2002
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Adiabatic quantum state generation and statistical zero knowledge
Dorit Aharonov and Amnon Ta-Shma · 2003
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Exponential algorithmic speedup by a quantum walk
Andrew M Childs, Richard Cleve, Enrico Deotto, Edward Farhi, Sam Gutmann, and Daniel A Spielman · 2003
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On asymptotics of large haar distributed unitary matrices
Dénes Petz and Júlia Réffy · 2004
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Feature selection and nearest centroid classification for protein mass spectrometry
Ilya Levner · 2005
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The concentration of measure phenomenon
Michel Ledoux · 2005
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Data clustering: 50 years beyond k-means
Anil K Jain · 2010
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Simulation of electronic structure hamiltonians using quantum computers
James D Whitfield, Jacob Biamonte, and Alán Aspuru-Guzik · 2011
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Importance sampling for a monte carlo matrix multiplication algorithm, with application to information retrieval
Sylvester Eriksson-Bique, Mary Solbrig, Michael Stefanelli, Sarah Warkentin, Ralph Abbey, and Ilse CF Ipsen · 2011
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Simulating quantum dynamics on a quantum computer
Nathan Wiebe, Dominic W Berry, Peter Høyer, and Barry C Sanders · 2011
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Hamiltonian simulation using linear combinations of unitary operations
Andrew M Childs and Nathan Wiebe · 2012
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Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators
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Esma Aïmeur, Gilles Brassard, and Sébastien Gambs · 2006
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Robust machine learning applied to astronomical data sets. iii. probabilistic photometric redshifts for galaxies and quasars in the sdss and galex
Nicholas M. Ball, Robert J. Brunner, Adam D. Myers, Natalie E. Strand, Stacey L. Alberts, and David Tcheng · 2008
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Quantum reinforcement learning
Daoyi Dong, Chunlin Chen, Hanxiong Li, and Tzyh-Jong Tarn · 2008
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Quantum random access memory
Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone · 2008
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Learning deep architectures for AI
Yoshua Bengio · 2009
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Data mining and machine learning in astronomy
Nicholas M Ball and Robert J Brunner · 2010
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Steven T Flammia, David Gross, Yi-Kai Liu, and Jens Eisert · 2012
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Quantum algorithms for supervised and unsupervised machine learning
Seth Lloyd, Masoud Mohseni, and Patrick Rebentrost · 2013
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Quantum support vector machine for big feature and big data classification
Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd · 2013
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Can quantum chemistry be performed on a small quantum computer?
Dave Wecker, Bela Bauer, Bryan K Clark, Matthew B Hastings, and Matthias Troyer · 2013
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UCI machine learning repository, 2013
K. Bache and M. Lichman · 2013
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http://about.usps.com/who-we-are/postal-facts/size-scope.htm/, 2014
2014
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Hamiltonian learning and certification using quantum resources
Nathan Wiebe, Christopher Granade, Christopher Ferrie, and DG Cory · 2014
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