New Local Explorations of the Unitary Coupled Cluster Energy Landscape

The
recent quantum information boom has effected a resurgence of
interest in the unitary coupled cluster (UCC) theory. Our group’s
interest in local energy landscapes of unitary ansätze prompted
us to investigate the classical approach of truncating
the Taylor series expansion (instead of a perturbative expansion)
of the UCC with singles and doubles (UCCSD) energy at the second order.
This amounts to an approach where the electron correlation energy
is estimated by taking a single Newton–Raphson step from Hartree–Fock
toward UCCSD. Such an approach has been explored previously, but the
accuracy was not extensively studied. In this paper, we investigate
the performance and observe similar pathologies to the linearized
coupled cluster with singles and doubles. We introduce the use of
derivatives of order three or greater to help partially recover the
variational lower bound of true UCCSD, restricting these derivatives
to those of the “unmixed” category in order to simplify
the model. By testing the approach on several potential energy surfaces
and reaction energies, we find this “diagonal” approximation
to higher order terms to be effective at reducing sensitivity near
singularities for strongly correlated regimes, while not significantly
diminishing the accuracy of weakly correlated systems.