Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansa''tze for Hybrid Variational Quantum Computing

One of the commonly used chemically inspired approachesin variationalquantum computing is the unitary coupled-cluster (UCC) ansa''tze.Despite being a systematic way of approaching the exact limit, thenumber of parameters in the standard UCC ansa''tze exhibits unfavorablescaling with respect to the system size, hindering its practical useon near-term quantum devices. Efforts have been taken to propose somevariants of the UCC ansa''tze with better scaling. In this paper,we explore the parameter redundancy in the preparation of unitarycoupled-cluster singles and doubles (UCCSD) ansa''tze employingspin-adapted formulation, small amplitude filtration, and entropy-basedorbital selection approaches. Numerical results of using our approachon some small molecules have exhibited a significant cost reductionin the number of parameters to be optimized and in the time to convergencecompared with conventional UCCSD-VQE simulations. We also discussthe potential application of some machine learning techniques in furtherexploring the parameter redundancy, providing a possible directionfor future studies.