Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth
This paper proposes a method of quantum Monte-Carlo integration that retains the full qua- dratic quantum advantage, without requiring any arithmetic or the quantum Fourier transform to be per- formed 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].