Adaptive Variational Quantum Simulations of Periodic Materials Using Qubit-Encoded Wave Functions

Materials design stands to be one of the most promising applications of quantum computing. However, the presence of noise in near-term quantum devices restricts quantum simulations of materials to shallow circuits. In this work, we present circuit-efficient variational quantum eigensolver (VQE) simulations of periodic materials using qubit-encoded wave functions based on Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) VQE. To iteratively construct accurate wave functions for periodic systems, we introduce operator pools comprising a complete set of anti-Hermitian one- and two-body qubit excitation/flipping operators. Numerical results demonstrate that these qubit-encoded algorithms can accurately predict the ground-state energy of periodic systems while significantly reducing circuit depth compared to Fermion-encoded algorithms. Additionally, we integrate the variance extrapolation technique with ADAPT-VQE algorithms to enhance the accuracy of ground-state energy estimations. This strategy further reduces the required circuit depth, enabling scalable and precise simulations of periodic systems.