Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth

Steven Herbert

doi:10.22331/q-2022-09-29-823

Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth

Steven Herbert

Quantinuum (Cambridge Quantum), Terrington House, 13-15 Hills Rd, Cambridge, CB2 1NL, UK
Department of Computer Science and Technology, University of Cambridge, UK

Published:	2022-09-29, volume 6, page 823
Eprint:	arXiv:2105.09100v4
Doi:	https://doi.org/10.22331/q-2022-09-29-823
Citation:	Quantum 6, 823 (2022).

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Abstract

This paper proposes a method of quantum Monte Carlo integration that retains the full quadratic quantum advantage, without requiring any arithmetic or quantum phase estimation to be performed on the quantum computer. No previous proposal for quantum Monte Carlo integration has achieved all of these at once. The heart of the proposed method is a Fourier series decomposition of the sum that approximates the expectation in Monte Carlo integration, with each component then estimated individually using quantum amplitude estimation. The main result is presented as theoretical statement of asymptotic advantage, and numerical results are also included to illustrate the practical benefits of the proposed method. The method presented in this paper is the subject of a patent application [Quantum Computing System and Method: Patent application GB2102902.0 and SE2130060-3].

► BibTeX data

@article{Herbert2022quantummontecarlo,
  doi = {10.22331/q-2022-09-29-823},
  url = {https://doi.org/10.22331/q-2022-09-29-823},
  title = {Quantum {M}onte {C}arlo {I}ntegration: {T}he {F}ull {A}dvantage in {M}inimal {C}ircuit {D}epth},
  author = {Herbert, Steven},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {823},
  month = sep,
  year = {2022}
}

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Cited by

[1] Koichi Miyamoto, "Quantum algorithms for numerical differentiation of expected values with respect to parameters", Quantum Information Processing 21 3, 109 (2022).

[2] Steven Herbert, "Quantum computing for data-centric engineering and science", Data-Centric Engineering 3, e36 (2022).

[3] Pierre-Yves Lagrave and Frédéric Barbaresco, MaxEnt 2022 17 (2022).

[4] Koichi Miyamoto, "Quantum algorithm for calculating risk contributions in a credit portfolio", EPJ Quantum Technology 9 1, 32 (2022).

[5] Sascha Wilkens and Joe Moorhouse, "Quantum computing for financial risk measurement", Quantum Information Processing 22 1, 51 (2023).

[6] Dylan Herman, Cody Googin, Xiaoyuan Liu, Alexey Galda, Ilya Safro, Yue Sun, Marco Pistoia, and Yuri Alexeev, "A Survey of Quantum Computing for Finance", arXiv:2201.02773, (2022).

[7] Kirill Plekhanov, Matthias Rosenkranz, Mattia Fiorentini, and Michael Lubasch, "Variational quantum amplitude estimation", Quantum 6, 670 (2022).

[8] Garrett T. Floyd, David P. Landau, and Michael R. Geller, "Quantum algorithm for Wang-Landau sampling", arXiv:2208.09543, (2022).

[9] M. C. Braun, T. Decker, N. Hegemann, and S. F. Kerstan, "Error Resilient Quantum Amplitude Estimation from Parallel Quantum Phase Estimation", arXiv:2204.01337, (2022).

[10] Koichi Miyamoto, "Quantum algorithm for calculating risk contributions in a credit portfolio", arXiv:2201.11394, (2022).

[11] Koichi Miyamoto, "Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation", arXiv:2108.09014, (2021).

[12] Philip Intallura, Georgios Korpas, Sudeepto Chakraborty, Vyacheslav Kungurtsev, and Jakub Marecek, "A Survey of Quantum Alternatives to Randomized Algorithms: Monte Carlo Integration and Beyond", arXiv:2303.04945, (2023).

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