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

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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].

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The above citations are from Crossref's cited-by service (last updated successfully 2024-07-15 09:04:06) and SAO/NASA ADS (last updated successfully 2024-07-15 09:04:07). The list may be incomplete as not all publishers provide suitable and complete citation data.