Numerical and geometrical aspects of flow-based variational quantum Monte Carlo
This is an incremental review aimed at researchers in machine learning and quantum information science.
The paper reviews flow-based variational quantum Monte Carlo techniques for simulating continuous-variable quantum systems, focusing on bosons in the quadrature basis and providing practical implementation guidance in PyTorch.
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.