  Quantum machine learning algorithms, the extensions of machine learning to
quantum regimes, are believed to be more powerful as they leverage the power of
quantum properties. Quantum machine learning methods have been employed to
solve quantum many-body systems and have demonstrated accurate electronic
structure calculations of lattice models, molecular systems, and recently
periodic systems. A hybrid approach using restricted Boltzmann machines and a
quantum algorithm to obtain the probability distribution that can be optimized
classically is a promising method due to its efficiency and ease of
implementation. Here we implement the benchmark test of the hybrid quantum
machine learning on the IBM-Q quantum computer to calculate the electronic
structure of typical 2-dimensional crystal structures: hexagonal-Boron Nitride
and graphene. The band structures of these systems calculated using the hybrid
quantum machine learning are in good agreement with those obtained by the
conventional electronic structure calculation. This benchmark result implies
that the hybrid quantum machine learning, empowered by quantum computers, could
provide a new way of calculating the electronic structures of quantum many-body
systems.
