Variational Quantum Boltzmann Machines

TL;DR

This paper introduces a variational quantum approach to training Quantum Boltzmann Machines that enables near-term implementation, allowing for efficient Gibbs state preparation and gradient evaluation on quantum hardware.

Contribution

It presents a novel variational method for Quantum Boltzmann Machines that supports arbitrary Hamiltonians and includes experimental validation on IBM Quantum hardware.

Findings

Successful numerical simulations of variational Gibbs states

Experimental validation on IBM Quantum hardware

Application to generative and discriminative learning tasks

Abstract

This work presents a novel realization approach to Quantum Boltzmann Machines (QBMs). The preparation of the required Gibbs states, as well as the evaluation of the loss function's analytic gradient is based on Variational Quantum Imaginary Time Evolution, a technique that is typically used for ground state computation. In contrast to existing methods, this implementation facilitates near-term compatible QBM training with gradients of the actual loss function for arbitrary parameterized Hamiltonians which do not necessarily have to be fully-visible but may also include hidden units. The variational Gibbs state approximation is demonstrated with numerical simulations and experiments run on real quantum hardware provided by IBM Quantum. Furthermore, we illustrate the application of this variational QBM approach to generative and discriminative learning tasks using numerical simulation.