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

Abstract

One of the commonly used chemically inspired approaches in variational quantum computing is the unitary coupledcluster (UCC) ansaẗze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC ansaẗze 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 the UCC ansaẗze with better scaling. In this paper, we explore the parameter redundancy in the preparation of unitary coupled-cluster singles and doubles (UCCSD) ansaẗze 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.

Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz

“…Thus, it seems the NFT optimizer can be migrated to the UCC ansatz straightforwardly. However, in closed-shell systems, which are commonly targeted by the UCC ansatz, UCC factors with complementary spin components are expected to share the same parameter. , In such cases, the number of energy evaluations required for an exact fit of the energy landscape increases to 14. This is because the analytic expression for E with respect to a single variable θ j has more parameters to be determined from measurements if two UCC factors share the same parameter θ j .…”

Physical Chemistry of Quantum Information Science

“…We investigate the topic of quantum algorithms tailored for quantum chemistry, molecular dynamics, and statistical mechanics. This includes a quest to enhance the accuracy of classical computations for difficult chemistry problems involving strongly correlated systems in the works by A. Tammaro et al., A. Khamoshi et al, and N. T. Le and L. N. Tran., and calculations of excited states in articles by Y. Kim and A. I. Krylov and by T. Yoshikura et al Outstanding problems of quantum state preparation were discussed by I. Magoulas and F. A. Evangelista, S. G. Mehendale et al, S. E. Ghasempouri et al, J. H. Zhang et al., and L. M. Sager-Smith et al, for near-term quantum algorithms. An equally important topic of quantum measurement is touched upon by Z. P. Bansingh et al and T. Kurita et al In addition, Hamiltonian learning from quantum dynamics is presented by R. Gupta et al, and an interesting and accessible approach to visualization of quantum algorithms is described by I. Ganti and S. S. Iyengar …”