Simulating periodic systems on quantum computer

TL;DR

This paper enhances quantum algorithms for simulating extended periodic systems by introducing modified VQE techniques and a combined VQE/QSE approach, achieving improved accuracy in modeling 1D hydrogen chains and their excited states.

Contribution

It proposes two novel schemes to improve the accuracy of quantum simulations for extended systems, addressing limitations of existing VQE algorithms.

Findings

Modified VQE avoids complex Hamiltonian issues.

VQE/QSE accurately models potential energy curves.

Excited states match FCI results closely.

Abstract

The variational quantum eigensolver (VQE) is one of the most appealing quantum algorithms to simulate electronic structure properties of molecules on near-term noisy intermediate-scale quantum devices. In this work, we generalize the VQE algorithm for simulating extended systems. However, the numerical study of an one-dimensional (1D) infinite hydrogen chain using existing VQE algorithms shows a remarkable deviation of the ground state energy with respect to the exact full configuration interaction (FCI) result. Here, we present two schemes to improve the accuracy of quantum simulations for extended systems. The first one is a modified VQE algorithm, which introduces an unitary transformation of Hartree-Fock orbitals to avoid the complex Hamiltonian. The second one is a Post-VQE approach combining VQE with the quantum subspace expansion approach (VQE/QSE). Numerical benchmark calculations demonstrate that both of two schemes provide an accurate enough description of the potential energy curve of the 1D hydrogen chain. In addition, excited states computed with the VQE/QSE approach also agree very well with FCI results.