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.

基于量子变分算法的最新方法可以成为解决量子多体问题的有力方法。然而，该领域的研究范围主要限于有机分子和简单的晶格模型。在这里，我们基于第一原理的有效模型构建，提出了周期系统的量子变分算法工作流程。以平均场近似的石墨烯 Hubbard 模型的能带结构为基准，基于受限玻尔兹曼机的变分量子本征求解器 (RBM-based VQE) 得到的计算本征值与精确的对角化结果吻合良好。几个 meV。