Numerical and geometrical aspects of flow-based variational quantum Monte Carlo

TL;DR

This paper reviews flow-based variational quantum Monte Carlo methods for simulating continuous-variable quantum systems, emphasizing geometrical and numerical aspects, and provides practical guidance for implementation.

Contribution

It offers a comprehensive overview of flow-based VQMC techniques, focusing on their geometric and numerical properties, with practical instructions for coding in PyTorch.

Findings

Stochastic estimation of time-dependent variational principles explained

Relationship between variational evolution and information geometry clarified

Practical implementation guidance provided for PyTorch code

Abstract

This article aims to summarize recent and ongoing efforts to simulate continuous-variable quantum systems using flow-based variational quantum Monte Carlo techniques, focusing for pedagogical purposes on the example of bosons in the field amplitude (quadrature) basis. Particular emphasis is placed on the variational real- and imaginary-time evolution problems, carefully reviewing the stochastic estimation of the time-dependent variational principles and their relationship with information geometry. Some practical instructions are provided to guide the implementation of a PyTorch code. The review is intended to be accessible to researchers interested in machine learning and quantum information science.