Variational quantum simulation for periodic materials

Nobuyuki Yoshioka,Wataru Mizukami,Takeshi Sato,Yuya O Nakagawa,Yu-Ya Ohnishi

doi:10.1103/physrevresearch.4.013052

Abstract

We present a quantum-classical hybrid algorithm that simulates electronic structures of periodic systems such as ground states and quasiparticle band structures. By extending the unitary coupled cluster (UCC) theory to describe crystals in arbitrary dimensions, for a hydrogen chain, we numerically demonstrate that the UCC ansatz implemented on a quantum circuit can be successfully optimized with a small deviation from the exact diagonalization over the entire range of the potential energy curves. Furthermore, by using the quantum subspace expansion method, in which we truncate the Hilbert space within the linear response regime from the ground state, the quasiparticle band structure is computed as charged excited states. Our work establishes a powerful interface between the rapidly developing quantum technology and modern material science.

Highlights

Achieving decisive ab initio descriptions of electronic properties in solid systems is one of the most significant issues in modern material science
SUMMARY AND OUTLOOK We have presented a framework for simulating the electronic structures of solids using noisy intermediate-scale quantum (NISQ)
The numerical results demonstrate that our variational quantum eigensolver (VQE)-based algorithm simulates the hydrogen chain well, in the weakly correlated electronic structures and for the strongly correlated regimes

Summary

INTRODUCTION

Achieving decisive ab initio descriptions of electronic properties in solid systems is one of the most significant issues in modern material science. The growth of computational resources requirements rapidly exceeds supercomputing capacity, which severely limits the exploration of realistic materials. Algorithms with both favorable scaling and high accuracy beyond the current schemes are indispensable. In the present work we propose and demonstrate that a VQE-based framework enables simulations of solid materials at the ab initio level. The present work establishes a powerful interface between two major fields, namely, the rapidly developing quantum computing technology and modern material science

SECOND QUANTIZED AB INITIO CRYSTAL HAMILTONIAN

VARIATIONAL QUANTUM EIGENSOLVER AND UNITARY COUPLED CLUSTER THEORY FOR SOLIDS

COMPUTING QUASIPARTICLE BANDS FROM THE VQE WAVE FUNCTION

NUMERICAL EXAMPLES

SUMMARY AND OUTLOOK