  The factorized form of unitary coupled cluster theory (UCC) is a promising
wave-function ansatz for the variational quantum eigensolver algorithm. Here,
we present a quantum inspired algorithm for UCC based on an exact operator
identity for the individual UCC factors. We implement this algorithm for
calculations of the H$_{10}$ linear chain and the H$_2$O molecule with single
and double $\zeta$ basis sets to provide insights about UCC as a wave-function
ansatz. We find that as an electronic structure method, UCC could potentially
be valuable for strongly correlated systems, for which conventional coupled
cluster theory has difficulties. On quantum computers, the factorized form of
UCC can also serve as an initial state preparation method for the quantum
phase-estimation algorithm, since it yields higher overlap with the ground
state than many other common variational ansatzes. This classical algorithm for
UCC also enables widespread testing of the technique, which will be useful for
benchmarking quantum computations.
