A Quantum Algorithm to Calculate Band Structure at the EOM Level of Theory

TL;DR

This paper introduces a quantum algorithm leveraging the EOM theory and an adaptive variational approach to efficiently compute the electronic band structure of materials, demonstrated on silicon and diamond.

Contribution

It presents a novel quantum algorithm combining ADAPT-C and EOM theory for accurate band structure calculations on quantum computers, improving computational efficiency.

Findings

Successfully simulated silicon and diamond band structures

Demonstrated the feasibility of the EOM-ADAPT-C protocol

Provided a proof of concept using a quantum computer simulator

Abstract

Band structure is a cornerstone to understand electronic properties of materials. Accurate band structure calculations using a high-level quantum-chemistry theory can be computationally very expensive. It is promising to speed up such calculations with a quantum computer. In this study, we present a quantum algorithm for band structure calculation based on the equation-of-motion (EOM) theory. First, we introduce a new variational quantum eigensolver algorithm named ADAPT-C for ground-state quantum simulation of solids, where the wave function is built adaptively from a complete set of anti-Hermitian operators. Then, on top of the ADAPT-C ground state, quasiparticle energies and the band structure can be calculated using the EOM theory in a quantum-subspace-expansion (QSE) style, where the projected excitation operators guarantee that the killer condition is satisfied. As a proof of principle, such an EOM-ADAPT-C protocol is used to calculate the band structures of silicon and diamond using a quantum computer simulator.