Quantum Boltzmann Machine

TL;DR

This paper introduces a quantum Boltzmann Machine (QBM) based on quantum distributions, proposing a sampling-based training method with bounds to handle quantum complexities, and explores its potential with quantum annealing hardware.

Contribution

It presents the first framework for training quantum Boltzmann Machines using bounds on quantum probabilities, enabling efficient sampling-based training.

Findings

QBM training can be performed with and without bounds.

Comparison shows QBM can match classical Boltzmann performance.

Potential for implementation on quantum annealing hardware like D-Wave.

Abstract

Inspired by the success of Boltzmann Machines based on classical Boltzmann distribution, we propose a new machine learning approach based on quantum Boltzmann distribution of a transverse-field Ising Hamiltonian. Due to the non-commutative nature of quantum mechanics, the training process of the Quantum Boltzmann Machine (QBM) can become nontrivial. We circumvent the problem by introducing bounds on the quantum probabilities. This allows us to train the QBM efficiently by sampling. We show examples of QBM training with and without the bound, using exact diagonalization, and compare the results with classical Boltzmann training. We also discuss the possibility of using quantum annealing processors like D-Wave for QBM training and application.