Toward the “platinum standard” of quantum chemistry on quantum computers: Perturbative quadruple corrections in unitary coupled cluster theory

We propose a non-iterative, post-hoc correction to the unitary coupled cluster theory with the single, double, and triple excitations (UCCSDT) Ansatz, which considers the leading-order effects of neglected quadruple excitations. We present two ways to derive this correction, henceforth referred to as [Q-6], which leads to an improvement in the correlation energy shown to be truncated to sixth-order in many-body perturbation theory. A comparison between the UCC-based [Q-6] correction proposed in this work and analogous, "platinum standard" quadruple corrections proposed in conventional coupled cluster 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 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.