Toward the "platinum standard" of quantum chemistry on quantum computers: perturbative quadruple corrections in unitary coupled cluster theory

TL;DR

This paper introduces a non-iterative quadruples correction to unitary coupled cluster theory, improving correlation energy calculations in quantum chemistry and achieving chemical accuracy in small molecule potential energy surfaces.

Contribution

It presents a novel quadruples correction [Q-6] for UCCSDT that is derived from many-body perturbation theory and is distinct from prior corrections, enhancing quantum chemistry accuracy.

Findings

[Q-6] improves correlation energy estimates.

t/UCCSDT[Q-6] achieves chemical accuracy.

Correction is constructed from internally connected components.

Abstract

We propose a non-iterative, post hoc correction to the unitary coupled cluster theory with single, double, and triple excitations (UCCSDT) ansatz, which considers the leading-order effects of neglected quadruple excitations. We present two ways to derive this quadruples correction to UCCSDT, henceforth referred to as [Q-6], which leads to an improvement in the correlation energy shown to be correct through sixth-order in many-body perturbation theory (MBPT). A comparison between the UCC-based [Q-6] correction proposed in this work and analogous, "platinum" standard quadruples corrections proposed in conventional coupled cluster (CC) theory recognizes that [Q-6] is distinct from prior corrections since it is constructed entirely from internally connected components. Although Trotterized (t) and full operator variants of UCCSDT exhibit errors in scans of small molecule potential energy surfaces (PESs) that routinely exceed 1.6 mH, we find that t/UCCSDT[Q-6] is nevertheless able to achieve chemical accuracy as measured by the mean-unsigned error (MUE).