Boltzmann machine learning with a variational quantum algorithm

TL;DR

This paper introduces a quantum algorithm using NISQ devices to efficiently perform Boltzmann machine learning by approximating thermal states through variational imaginary time simulation, demonstrated via numerical simulations.

Contribution

It presents a novel quantum approach for Boltzmann machine learning that reduces computational complexity using variational imaginary time simulation on NISQ devices.

Findings

Numerical simulations confirm the effectiveness of the quantum scheme.

The method accurately approximates thermal equilibrium states.

The approach is feasible with current NISQ technology.

Abstract

Boltzmann machine is a powerful tool for modeling probability distributions that govern the training data. A thermal equilibrium state is typically used for Boltzmann machine learning to obtain a suitable probability distribution. The Boltzmann machine learning consists of calculating the gradient of the loss function given in terms of the thermal average, which is the most time consuming procedure. Here, we propose a method to implement the Boltzmann machine learning by using Noisy Intermediate-Scale Quantum (NISQ) devices. We prepare an initial pure state that contains all possible computational basis states with the same amplitude, and apply a variational imaginary time simulation. Readout of the state after the evolution in the computational basis approximates the probability distribution of the thermal equilibrium state that is used for the Boltzmann machine learning. We actually perform the numerical simulations of our scheme and confirm that the Boltzmann machine learning works well by our scheme.