A variational quantum eigensolver tailored to multi-band tight-binding simulations of electronic structures

TL;DR

This paper introduces a cost-efficient VQE measurement scheme tailored for multi-band tight-binding electronic structure simulations, significantly reducing measurement complexity and demonstrating superior efficiency over existing methods.

Contribution

It presents a novel measurement scheme for VQE that leverages lattice geometry and extended Bell measurements, improving efficiency for tight-binding electronic structure calculations.

Findings

Accurately computes band-gap energies of perovskite supercells.

Reduces the number of measurement circuits compared to Pauli grouping methods.

Demonstrates practical applicability for 3D atomic structures on NISQ devices.

Abstract

We propose a cost-efficient measurement scheme of the variational quantum eigensolver (VQE) for atomistic simulations of electronic structures based on a tight-binding (TB) theory. Leveraging the lattice geometry of a material domain, the sparse TB Hamiltonian is constructed in a bottom-up manner and is represented as a linear combination of the standard-basis (SB) operators. The cost function is evaluated with an extended version of the Bell measurement circuit that can simultaneously measure multiple SB operators and therefore reduces the number of circuits required bythe evaluation process. The proposed VQE scheme is applied to find band-gap energies of metal-halide-perovskite supercells that have finite dimensions with closed boundaries and are described with a sp3 TB model. Experimental results confirm that the proposed scheme gives solutions that follow well the accurate ones, but, more importantly, has the computing efficiency that is obviously superior to the commutativity-based Pauli grouping methods. Extending the application scope of VQE to three-dimensional confined atomic structures, this work can serve as a practical guideline for handling TB simulations in the noise-intermediate-scale quantum devices.