  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.
