A new "gold standard": perturbative triples corrections in unitary coupled cluster theory and prospects for quantum computing

A major difficulty in quantum simulation is the adequate treatment of a large collection of entangled particles, synonymous with electron correlation in electronic structure theory, with coupled cluster (CC) theory being the leading framework in dealing with this problem. Augmenting computationally affordable low-rank approximations in CC theory with a perturbative account of higher-rank excitations is a tractable and effective way of accounting for the missing electron correlation in those approximations. This is perhaps best exemplified by the "gold standard" CCSD(T) method, which bolsters the baseline CCSD with effects of triple excitations using considerations from many-body perturbation theory (MBPT). Despite this established success, such a synergy between MBPT and the unitary analog of CC theory (UCC) has not been explored. In this work, we propose a similar approach wherein converged UCCSD amplitudes, which can be obtained on a quantum computer, are leveraged by a classical computer to evaluate energy corrections associated with triple excitations - leading to the UCCSD[T] and UCCSD(T*) methods. The rationale behind these choices is shown to be rigorous by studying the properties of finite-order UCC energy functionals. Although our efforts do not support the addition of the fifth-order contribution as in the (T) correction, comparisons are nevertheless made using a hybrid UCCSD(T) approach. We assess the performance of these approaches on a collection of small molecules, and demonstrate the benefits of harnessing the inherent synergy between MBPT and UCC theories.