Boltzmann machine learning with a variational quantum algorithm

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.

Researchers at Tokyo University of Science and National Institute of Advanced Industrial Science and Technology (AIST), Japan, propose a method to implement the Boltzmann machine learning by using Noisy Intermediate-Scale Quantum (NISQ) devices.

They prepared an initial pure state that contains all possible computational basis states with the same amplitude, and applied a variational imaginary time simulation. Readout of the state after the evolution in the computational basis approximated the probability distribution of the thermal equilibrium state that is used for the Boltzmann machine learning.

They actually performed the numerical simulations of their scheme and confirmed that the Boltzmann machine learning works well.

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