Low-Depth Unitary Coupled Cluster Theory for Quantum Computation

TL;DR

This paper introduces a Taylor expansion approach to reduce the circuit depth of unitary coupled cluster methods in quantum computing, especially effective for weakly correlated molecules, balancing accuracy and resource requirements.

Contribution

It proposes a novel Taylor expansion algorithm for UCC that decreases circuit depth by approximating small amplitudes, with selective exact treatment of strongly correlated factors.

Findings

Effective for weakly correlated molecules near equilibrium

Requires fewer quantum resources compared to standard UCC

Maintains accuracy with minimal exact factors as correlations increase

Abstract

The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems with many orbitals, the required number of UCC factors still leads to very deep quantum circuits, which can be challenging to implement. Based on the observation that most UCC amplitudes are small for weakly correlated molecules, we devise an algorithm that employs a Taylor expansion in the small amplitudes, trading off circuit depth for extra measurements. Strong correlations can be taken into account by performing the expansion about a small set of UCC factors, which are treated exactly. Near equilibrium, the Taylor series expansion often works well without the need to include any exact factors; as the molecule is stretched and correlations increase, we find only a small number of factors need to be treated exactly.