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A major difficulty in quantum simulation is the adequate treatment of a largecollection of entangled particles, synonymous with electron correlation inelectronic structure theory, with coupled cluster (CC) theory being the leadingframework in dealing with this problem. Augmenting computationally affordablelow-rank approximations in CC theory with a perturbative account of higher-rankexcitations is a tractable and effective way of accounting for the missingelectron correlation in those approximations. This is perhaps best exemplifiedby the "gold standard" CCSD(T) method, which bolsters the baseline CCSD witheffects of triple excitations using considerations from many-body perturbationtheory (MBPT). Despite this established success, such a synergy between MBPTand 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 beobtained on a quantum computer, are leveraged by a classical computer toevaluate energy corrections associated with triple excitations - leading to theUCCSD[T] and UCCSD(T*) methods. The rationale behind these choices is shown tobe rigorous by studying the properties of finite-order UCC energy functionals.Although our efforts do not support the addition of the fifth-ordercontribution as in the (T) correction, comparisons are nevertheless made usinga hybrid UCCSD(T) approach. We assess the performance of these approaches on acollection of small molecules, and demonstrate the benefits of harnessing theinherent synergy between MBPT and UCC theories.

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