Reducing Unitary Coupled Cluster Circuit Depth by Classical Stochastic Amplitude Pre-Screening

TL;DR

This paper introduces a hybrid classical-quantum method that uses stochastic classical pre-screening to identify important excitations, significantly reducing quantum circuit depth in UCC-based VQE calculations for quantum chemistry.

Contribution

A novel combined classical-stochastic and quantum approach that reduces circuit depth by pre-selecting excitations, improving efficiency for quantum chemistry simulations.

Findings

Achieved sub-milliHartree accuracy in molecular energy calculations.

Significantly reduced quantum circuit depth and resource requirements.

Demonstrated systematic improvability of the approximation.

Abstract

Unitary Coupled Cluster (UCC) approaches are an appealing route to utilising quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared to the exponential scaling required on classical computers. Current noisy intermediate scale quantum (NISQ) computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the Variational Quantum Eigensolver (VQE) approach. We present a combined classical--quantum approach where a stochastic classical UCC pre-processing step is used to determine the important excitations in the UCC ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with simulations on the CH$_2$, N$_2$ and N$_2$H$_2$ molecules giving sub-milliHartree errors.