Quantum Computation of Electronic Structure with Projector Augmented-Wave Method and Plane Wave Basis Set

Quantum simulation of materials is a promising application area of quantum computers. To practically realize this promise, we must reduce quantum resources while maintaining accuracy. In electronic structure calculations on classical computers, resource reduction has been achieved by using the projector augmented-wave method (PAW) and plane wave basis sets. However, the PAW method generalized for many-body states introduces non-orthogonality effects which impede its direct application to quantum computing. In this work, we develop a unitary variant of the PAW (UPAW) that preserves the orthogonality constraints. We provide a linear-combination-of-unitaries decomposition of the UPAW Hamiltonian to enable ground state estimation using qubitized quantum phase estimation. Additionally, we further improve algorithmic efficiency by extending classical down-sampling techniques into the quantum setting. We then estimate quantum resources for crystalline solids to estimate the energy within chemical accuracy with respect to the full basis set limit, and also consider a supercell approach which is more suitable for calculations of defect states. We provide the quantum resources for energy estimation of a nitrogen-vacancy defect centre in diamond which is a challenging system for classical algorithms and a quintessential problem in the studies of quantum point defects.