Variational inference with a quantum computer

TL;DR

This paper introduces a quantum-based variational inference method using Born machines, enabling efficient approximation of complex distributions in Bayesian networks and demonstrating practical implementation on a quantum computer.

Contribution

It proposes using quantum Born machines as variational distributions within operator variational inference, a novel approach for quantum-enhanced probabilistic inference.

Findings

Successfully applied to Bayesian networks

Implemented on IBM quantum hardware

Enables inference with distributions beyond classical capabilities

Abstract

Inference is the task of drawing conclusions about unobserved variables given observations of related variables. Applications range from identifying diseases from symptoms to classifying economic regimes from price movements. Unfortunately, performing exact inference is intractable in general. One alternative is variational inference, where a candidate probability distribution is optimized to approximate the posterior distribution over unobserved variables. For good approximations, a flexible and highly expressive candidate distribution is desirable. In this work, we use quantum Born machines as variational distributions over discrete variables. We apply the framework of operator variational inference to achieve this goal. In particular, we adopt two specific realizations: one with an adversarial objective and one based on the kernelized Stein discrepancy. We demonstrate the approach numerically using examples of Bayesian networks, and implement an experiment on an IBM quantum computer. Our techniques enable efficient variational inference with distributions beyond those that are efficiently representable on a classical computer.