On the learning abilities of photonic continuous-variable Born machines

TL;DR

This paper explores the training of photonic continuous-variable Born machines (CVBMs) using stochastic gradients with limited samples, enabled by a novel classical simulation method for homodyne detection, advancing understanding of their learning capabilities.

Contribution

Introduces a new classical simulation strategy for homodyne detection, enabling larger-scale training of multimode CVBMs and analysis of their learning abilities with stochastic gradients.

Findings

Successful training of multimode CVBMs demonstrated.

Effective stochastic gradient-based learning achieved.

Classical simulation method facilitates larger quantum distribution modeling.

Abstract

This paper investigates photonic continuous-variable Born machines (CVBMs), which utilize photonic quantum states as resources for continuous probability distributions. Implementing exact gradient descent in the CVBM training process is often infeasible, bringing forward the need to approximate the gradients using an estimator obtained from a smaller number of samples, obtaining a quantum stochastic gradient descent (SGD) method. In this work, the ability to train CVBMs is analyzed using stochastic gradients obtained using relatively few samples from the probability distribution corresponding to homodyne measurement. The main obstacle to this analysis is that classically simulating CVBMs and obtaining samples is a demanding task, while a large number of iterations are needed to achieve convergence. The present research is enabled by a novel strategy to simulate homodyne detections of generic multimode photonic states using a classical computer. With this approach, a more comprehensive study of CVBMs is made possible, and the training of multimode CVBMs is demonstrated with parametric quantum circuits considerably larger than in previous articles. More specifically, we use the proposed algorithm to demonstrate learning of multimode quantum distributions using CVBMs. Moreover, successful CVBM trainings were demonstrated with the use of stochastic gradients.