Variational quantum eigensolver for closed-shell molecules with non-bosonic corrections

TL;DR

This paper introduces a non-bosonic correction scheme for the variational quantum eigensolver (VQE) that improves quantum chemistry simulations on NISQ devices by reducing qubit requirements and accounting for non-paired electron excitations.

Contribution

It proposes a simple correction method for VQE that incorporates non-bosonic effects, enabling accurate simulations with fewer qubits in the seniority-zero approximation.

Findings

Accurately computed ground state energies for H2O, N2, and Li2O.

Achieved results with only 6 to 12 qubits, significantly fewer than traditional methods.

Demonstrated good agreement with full configuration interaction models.

Abstract

The realization of quantum advantage with noisy-intermediate-scale quantum (NISQ) machines has become one of the major challenges in computational sciences. Maintaining coherence of a physical system with more than ten qubits is a critical challenge that motivates research on compact system representations to reduce algorithm complexity. Toward this end, quantum simulations based on the variational quantum eigensolver (VQE) is considered to be one of the most promising algorithms for quantum chemistry in the NISQ era. We investigate reduced mapping of one spatial orbital to a single qubit to analyze the ground state energy in a way that the Pauli operators of qubits are mapped to the creation/annihilation of singlet pairs of electrons. To include the effect of non-bosonic (or non-paired) excitations, we introduce a simple correction scheme in the electron correlation model approximated by the geometrical mean of the bosonic (or paired) terms. Employing it in a VQE algorithm, we assess ground state energies of H2O, N2, and Li2O in good agreements with full configuration interaction (FCI) models respectively, using only 6, 8, and 12 qubits with quantum gate depths proportional to the squares of the qubit counts. With the adopted seniority-zero approximation that uses only one half of the qubit counts of a conventional VQE algorithm, we find our non-bosonic correction method reaches reliable quantum chemistry simulations at least for the tested systems.