Parameter Redundancy in the Unitary Coupled-Cluster Ansatze for Hybrid Variational Quantum Computing

Abstract

One of the commonly used chemical-inspired approaches in variational quantum computing is the unitary coupledcluster (UCC) ansatze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC ansatze exhibits unfavorable scaling with respect to the system size, hindering its practical use on near-term quantum devices. Efforts have been taken to propose some variants of UCC ansatze with better scaling. In this paper we explore the parameter redundancy in the preparation of unitary coupled-cluster singles and doubles (UCCSD) ansatze employing spin-adapted formulation, small amplitude filtration, and entropy-based orbital selection approaches. Numerical results of using our approach on some small molecules have exhibited a significant cost reduction in the number of parameters to be optimized and in the time to convergence compared with conventional UCCSD-VQE simulations. We also discuss the potential application of some machine learning techniques in further exploring the parameter redundancy, providing a possible direction for future studies.

Machine Learning Aided Dimensionality Reduction towards a Resource Efficient Projective Quantum Eigensolver

“…We will refer our scheme as ML aided PQE(ML-PQE). In this context we must mention that certain other downfolding techniques have been recently developed to solve classical coupled cluster theory using some sub-system embedding subalgebra (SES) techniques [37][38][39][40][41] and later extended to quantum computing framework as well [42][43][44][45][46].…”