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Open Access

On Quantum Methods for Machine Learning Problems Part I: Quantum Tools

College of Computer Science & Software Engineering, Shenzhen University, Shenzhen 518000, China.
Kazan Federal University, Kazan 42008, Russia.
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Abstract

This is a review of quantum methods for machine learning problems that consists of two parts. The first part, "quantum tools", presents the fundamentals of qubits, quantum registers, and quantum states, introduces important quantum tools based on known quantum search algorithms and SWAP-test, and discusses the basic quantum procedures used for quantum search methods. The second part, "quantum classification algorithms", introduces several classification problems that can be accelerated by using quantum subroutines and discusses the quantum methods used for classification.

References

[1]
S. Arunachalam and R. de Wolf, Guest column: A survey of quantum learning theory, ACM SIGACT News, vol. 48, no. 2, pp. 41-67, 2017.
[2]
D. Kopczyk, Quantum machine learning for data scientists, arXiv preprint arXiv: 1804.10068, 2018.
[3]
M. Schuld, I. Sinayskiy, and F. Petruccione, An introduction to quantum machine learning, Contemporary Physics, vol. 56, no. 2, pp. 172-185, 2015.
[4]
M. Schuld, I. Sinayskiy, and F. Petruccione, The quest for a quantum neural network, Quantum Information Processing, vol. 13, no. 11, pp. 2567-2586, 2014.
[5]
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge, UK: Cambridge University Press, 2000.
[7]
A. Eremenko, Spectral theorems for hermitian and unitary matrices, Technical report, Purdue University, USA, 2017.
[8]
I. Wegener, Branching Programs and Binary Decision Diagrams: Theory and Applications. Philadelphia, PA, USA: SIAM, 2000.
[9]
F. Ablayev, A. Gainutdinova, and M. Karpinski, On computational power of quantum branching programs, in Fundamentals of Computation Theory. FCT 2001, R. Freivalds, ed. Berlin, Germany: Springer, 2001, pp. 59-70.
[10]
F. M. Ablayev and A. V. Vasilyev, On quantum realisation of Boolean functions by the fingerprinting technique, Discrete Mathematics and Applications, vol. 19, no. 6, pp. 555-572, 2009.
[11]
F. Ablayev, M. Ablayev, K. Khadiev, and A. Vasiliev, Classical and quantum computations with restricted memory, in Adventures Between Lower Bounds and Higher Altitudes, 2018, pp. 129-155.
[12]
C. A. Trugenberger, Probabilistic quantum memories, Physical Review Letters, vol. 87, no. 6, p. 067901, 2001.
[13]
P. Kaye, Reversible addition circuit using one ancillary bit with application to quantum computing, arXiv preprint arXiv: quant-ph/0408173, 2004.
[14]
L. K. Grover, A fast quantum mechanical algorithm for database search, in ACM Symp. on Theory of Computing, Philadelphia, PA, USA, 1996, pp. 212-219.
[15]
G. Brassard, P. Høyer, M. Mosca, and A. Tapp, Quantum amplitude amplification and estimation, Contemporary Mathematics, vol. 305, pp. 53-74, 2002.
[16]
L. K. Grover and J. Radhakrishnan, Is partial quantum search of a database any easier, in ACM Symp. on Parallelism in Algorithms and Architectures, Las Vegas, NV, USA, 2005, pp. 186-194.
[17]
M. Boyer, G. Brassard, P. Høyer, and A. Tapp, Tight bounds on quantum searching, Fortschritte der Physik, vol. 46, nos. 4&5, pp. 493-505, 1998.
[18]
G. Brassard, P. Høyer, and A. Tapp, Quantum counting, in International Colloquium on Automata, Languages, and Programming, K. G. Larsen, S. Skyum, and G. Winskel, eds. Berlin, Germany: Springer, 1998, pp. 820-831.
[19]
P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Journal on Computing, vol. 26, no. 5, pp. 1484-1509, 1997.
[20]
P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Review, vol. 41, no. 2, pp. 303-332, 1999.
[21]
A. Y. Kitaev, Quantum measurements and the abelian stabilizer problem, arXiv preprint arXiv: quant-ph/ 9511026, 1995.
[22]
R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, Quantum algorithms revisited, in Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 454, no. 1969, pp. 339-354, 1998.
[23]
M. Mosca, Counting by quantum eigenvalue estimation, Theoretical Computer Science, vol. 264, no. 1, pp. 139-153, 2001.
[24]
N. Wiebe, A. Kapoor, and K. M. Svore, Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning, Quantum Information & Computation, vol. 15, nos. 3&4, pp. 316-356, 2015.
[25]
C. Durr and P. Høyer, A quantum algorithm for finding the minimum, arXiv preprint arXiv: quant-ph/9607014, 1996.
[26]
D. Gottesman and I. Chuang, Quantum digital signatures, arXiv preprint arXiv: quant-ph/0105032, 2001.
[27]
F. M. Ablayev and A. V. Vasiliev, Cryptographic quantum hashing, Laser Physics Letters, vol. 11, no. 2, p. 025202, 2014.
[28]
Project Q, https://projectq.ch/, 2019.
[29]
Qiskit, https://qiskit.org/, 2019.
[30]
[32]
The quipper language, https://www.mathstat.dal.ca/selinger/quipper/, 2019.
Big Data Mining and Analytics
Pages 41-55
Cite this article:
Ablayev F, Ablayev M, Huang JZ, et al. On Quantum Methods for Machine Learning Problems Part I: Quantum Tools. Big Data Mining and Analytics, 2020, 3(1): 41-55. https://doi.org/10.26599/BDMA.2019.9020016

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Received: 10 September 2019
Accepted: 25 September 2019
Published: 19 December 2019
© The author(s) 2020

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).

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