Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?

TL;DR

This paper evaluates quantum orbital-optimized UCC methods for strongly correlated systems, demonstrating their potential to outperform classical methods in capturing complex electronic behaviors with fewer quantum resources.

Contribution

It introduces and assesses variants of q-UCCSD with orbital optimization, showing their effectiveness in modeling strongly correlated molecules and systems.

Findings

q-UCC variants accurately model dissociation profiles of H4, H2O, N2

Orbital optimization enhances the ability of q-UCC to handle strong correlations

Results suggest quantum algorithms can outperform classical methods in challenging cases

Abstract

The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum UCC with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the Variational Quantum Eigensolver (VQE) algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems such as H$_4$, H$_2$O and N$_2$ molecules, as well as the one-dimensional periodic Fermi-Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.