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

A state of the art method based on quantum variational algorithms can be a powerful approach for solving quantum many-body problems. However, the research scope in the field is mainly limited to organic molecules and simple lattice models. Here, we propose a workflow of a quantum variational algorithm 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 obtained by restricted Boltzmann machine-based variational quantum eigensolver (RBM-based VQE) show good agreement with the exact diagonalization results within a few meV. 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.