Photonic quantum algorithm for Monte Carlo integration

TL;DR

This paper introduces a photonic quantum algorithm using continuous variables to perform multi-dimensional Monte Carlo integration, achieving quadratic speedup over classical methods by adapting amplitude estimation.

Contribution

It develops a novel continuous-variable quantum algorithm for Monte Carlo integration, including error analysis and finite squeezing effects, demonstrating its practical advantages.

Findings

Quadratic speedup in Monte Carlo integration using photonic quantum algorithms

Effective encoding of multi-dimensional integrals into optical modes

Feasibility of continuous-variable quantum algorithms for numerical integration

Abstract

We present a continuous-variable photonic quantum algorithm for the Monte Carlo evaluation of multi-dimensional integrals. Our algorithm encodes n-dimensional integration into n+3 modes and can provide a quadratic speedup in runtime compared to the classical Monte Carlo approach. The speedup is achieved by developing a continuous-variable adaptation of amplitude estimation. We provide an error analysis for each element of the algorithm and account for the effects of finite squeezing. Our findings show that Monte Carlo integration is a natural use case for algorithms using the continuous-variable setting.