Many-body calculations for periodic materials via restricted Boltzmann machine-based VQE

A state-of-the-art method that combines a quantum computational algorithm and machine learning, so-called quantum machine learning, can be a powerful approach for solving quantum many-body problems. However, the research scope in the field was mainly limited to organic molecules and simple lattice models. Here, we propose a workflow of quantum machine learning applications for periodic systems on the basis of an effective model construction from first principles. The band structures of the Hubbard model of graphene with the mean-field approximation are calculated as a benchmark, and the calculated eigenvalues show good agreement with the exact diagonalization results within a few meV by employing the transfer learning technique in quantum machine learning. The results show that the present computational scheme has the potential to solve many-body problems quickly and correctly for periodic systems using a quantum computer.