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

James Stokes, Brian Chen, Shravan Veerapaneni

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.