New Local Explorations of the Unitary Coupled Cluster Energy Landscape

TL;DR

This paper explores a classical truncation method of the UCCSD energy Taylor series, using higher-order derivatives to improve energy estimates and reduce sensitivity near singularities in strongly correlated systems.

Contribution

It introduces a diagonal approximation of higher-order derivatives in the Taylor series expansion of UCCSD energy, enhancing classical energy estimation methods.

Findings

Effective at reducing sensitivity near singularities in strongly correlated regimes

Maintains accuracy for weakly correlated systems

Provides insights into local energy landscape exploration

Abstract

The recent quantum information boom has effected a resurgence of interest in unitary coupled cluster (UCC) theory. Our group's interest in local energy landscapes of unitary ans\"atze prompted us to investigate the classical approach of truncating the Taylor series expansion (instead of a perturbative expansion) of UCCSD energy at second-order. This amounts to an approach where 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 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.