Capabilities and Limits of the Unitary Coupled-cluster Approach with Generalized Two-body Cluster Operators

TL;DR

This paper investigates the use of generalized two-body excitation operators in unitary coupled-cluster methods for quantum chemistry, showing they can achieve high accuracy with compactness, especially in strongly correlated regimes, but with convergence challenges.

Contribution

It introduces and evaluates a generalized two-body excitation ansatz in unitary coupled-cluster methods, demonstrating its effectiveness and limitations compared to standard approaches.

Findings

Two-body operators with particle-hole excitation level one yield accurate, compact wavefunctions.

Generalized two-body operators with zero excitation rank are less effective.

The approach can match or surpass three-body excitation accuracy in strong correlation regimes.

Abstract

Unitary cluster expansions of the electronic wavefunction have recently gained much interest because of their use in conjunction with quantum algorithms. In this contribution, we investigate some aspects of an ansatz using generalized two-body excitations operators, which has been considered in some recent works on quantum algorithms for quantum chemistry. Our numerical results show that in particular two-body operators with effective particle-hole excitation level of one in connection with the usual particle-hole double excitation operators lead to a very accurate yet compact representation of the wavefunction. Generalized two-body operators with effective excitation rank zero have a considerably less pronounced effect. We compare to standard and unitary coupled-cluster expansions and show that the above mentioned approach matches or even surpasses the accuracy of expansions with three-body particle-hole excitations, in particular at the onset of strong correlation. A downside of the approach is that it is rather difficult to rigorously converge it to its variational minimum.