Dual Exponential Coupled Cluster Theory: Unitary Adaptation, Implementation in the Variational Quantum Eigensolver Framework and Pilot Applications

TL;DR

This paper introduces a unitary double exponential coupled cluster method adapted for the variational quantum eigensolver, capable of capturing high-rank connected excitations efficiently on quantum hardware.

Contribution

It develops a novel unitary variant of double exponential coupled cluster theory suitable for quantum computing, with multiple ansatz variants for enhanced expressibility.

Findings

Performs well across molecular potential energy surfaces

Requires shallow quantum circuits for implementation

Comparable accuracy to traditional coupled cluster methods

Abstract

In this paper, we have developed a unitary variant of a double exponential coupled cluster theory, which is capable of mimicking the effects of connected excitations of arbitrarily high rank, using only rank-one and rank-two parametrization of the wavefunction ansatz. While its implementation in a classical computer necessitates the construction of an effective Hamiltonian which involves infinite number of terms with arbitrarily high many-body rank, the same can easily be implemented in the hybrid quantum-classical variational quantum eigensolver framework with a reasonably shallow quantum circuit. The method relies upon the nontrivial action of a unitary, containing a set of rank-two scattering operators, on entangled states generated via cluster operators. We have further introduced a number of variants of the ansatz with different degrees of expressibility by judiciously approximating the scattering operators. With a number of applications on strongly correlated molecules, we have shown that all our schemes can perform uniformly well throughout the molecular potential energy surface without significant additional implementation cost and quantum complexity over the unitary coupled cluster approach with single and double excitations.