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We give an algorithm for prediction on a quantum computer which is based on a linear regression model with least squares optimisation.
Singular value decomposition and least squares solutions
Gene H Golub and Christian Reinsch · 1970
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Numerical linear algebra
Lloyd N Trefethen and David Bau III · 1997
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Creating superpositions that correspond to efficiently integrable probability distributions, 2002
Lov Grover and Terry Rudolph · 2002
Earlier work this paper cites.
Pattern recognition and machine learning
Christopher M Bishop · 2006
Earlier work this paper cites.
Handbook of linear algebra
Leslie Hogben · 2006
Earlier work this paper cites.
Quantum random access memory
Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone · 2008
Earlier work this paper cites.
Computational complexity: A modern approach
Sanjeev Arora and Boaz Barak · 2009
Earlier work this paper cites.
Quantum algorithm for linear systems of equations
Aram W Harrow, Avinatan Hassidim, and Seth Lloyd · 2009
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Quantum algorithm for data fitting
Nathan Wiebe, Daniel Braun, and Seth Lloyd · 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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Preconditioned quantum linear system algorithm
B David Clader, Bryan C Jacobs, and Chad R Sprouse · 2013
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Bryan O’Gorman, R Babbush, A Perdomo-Ortiz, Alan Aspuru-Guzik, and Vadim Smelyanskiy · 2015
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How to simulate a perceptron using quantum circuits
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Quantum assisted gaussian process regression
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Nathan Wiebe, Ashish Kapoor, and Krysta Svore · 2014
Cited alongside, same era.
Quantum support vector machine for big data classification
Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd · 2014
Cited alongside, same era.
See for example Yann LeCun’s list of the performance of different machine learning methods on the MNIST handwritten digits database: yann.lecun.com/exdb/mnist
Cited in the paper.
In machine learning applications, a regularisation term favouring small parameters is usually added to avoid overfitting. It is an interesting question for further research whether the normalisation condition for quantum states (i.e., containing the parameters as in WBL) can be harvested to introduce an effective regularisation
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Scott Aaronson · 2015
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