Quantum self-learning Monte Carlo with quantum Fourier transform sampler

TL;DR

This paper introduces a quantum-inspired self-learning Monte Carlo method using quantum Fourier transform circuits, which is classically simulable and offers advantages over traditional approaches, demonstrated through numerical simulations.

Contribution

It presents a novel quantum Fourier transform-based sampler for self-learning Monte Carlo, bridging quantum computing and classical sampling methods.

Findings

Classically simulable quantum Fourier transform sampler

Advantages over conventional Monte Carlo methods

Numerical simulations demonstrate effectiveness

Abstract

The self-learning Metropolis-Hastings algorithm is a powerful Monte Carlo method that, with the help of machine learning, adaptively generates an easy-to-sample probability distribution for approximating a given hard-to-sample distribution. This paper provides a new self-learning Monte Carlo method that utilizes a quantum computer to output a proposal distribution. In particular, we show a novel subclass of this general scheme based on the quantum Fourier transform circuit; this sampler is classically simulable while having a certain advantage over conventional methods. The performance of this "quantum inspired" algorithm is demonstrated by some numerical simulations.