Boltzmann machine learning with a variational quantum algorithm

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.

14 pages, 11 figures

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• Variational Quantum Algorithms
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• Variational Quantum Boltzmann Machines
• A Quantum Approach to Classical Statistical Mechanics
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• Variational inference with a quantum computer
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• Simulating noisy variational quantum eigensolver with local noise models
• Variational secure cloud quantum computing
• Assisted quantum simulation of open quantum systems
• Calculation of Gibbs partition function with imaginary time evolution on near-term quantum computers
• Supervised Learning Guarantee for Quantum AdaBoost