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.

Automated summary

The unitary coupled-cluster (UCC) ansatz is a commonly used chemically inspired approach in variational quantum computing. However, the standard UCC ansatz has an unfavorable scaling of the number of parameters with respect to the system size, which hinders its practical use on near-term quantum devices. This paper explores the parameter redundancy in the preparation of the unitary coupled-cluster singles and doubles (UCCSD) ansatz and proposes techniques to reduce the number of parameters and improve convergence time. Experimental results on small molecules demonstrate significant cost reduction and faster convergence compared to conventional UCCSD-VQE simulations. The potential application of machine learning techniques in further exploring parameter redundancy is also discussed as a future direction for research.