Constructing Compact ADAPT Unitary Coupled-Cluster Ansatz with Parameter-Based Criterion

TL;DR

This work tackles the scalability of ADAPT-VQE for quantum chemistry by addressing operator redundancy and high measurement costs. It introduces Param-ADAPT-VQE, which replaces gradient-based operator selection with a parameter-based criterion, and adds a sub-Hamiltonian evaluation and hot-start optimization to reduce measurements and accelerate convergence. Numerical results on BeH2 and extended molecules (LiH, H2O, NH3) show Param-ADAPT-VQE achieves comparable or better accuracy with fewer excitation operators and substantial measurement-cost reductions, outperforming standard ADAPT-VQE. The method remains compatible with existing ADAPT-VQE variants and is supported by publicly available code.

Abstract

The adaptive derivative-assembled pseudo-trotter variational quantum eigensolver (ADAPT-VQE) is a promising hybrid quantum-classical algorithm for molecular ground state energy calculation, yet its practical scalability is hampered by redundant excitation operators and excessive measurement costs. To address these challenges, we propose Param-ADAPT-VQE, a novel improved algorithm that selects excitation operators based on a parameter-based criterion instead of the traditional gradient-based metric. This strategy effectively eludes redundant operators. We further develop a sub-Hamiltonian technique and integrate a hot-start VQE optimization strategy, achieving a significant reduction in measurement costs. Numerical experiments on typical molecular systems demonstrate that Param-ADAPT-VQE outperforms the original ADAPT-VQE in computational accuracy, ansatz size, and measurement costs. Furthermore, our scheme retains the fundamental framework of ADAPT-VQE and is thus fully compatible with its various modified versions, enabling further performance improvements in specific aspects. This work presents an efficient and scalable enhancement to ADAPT-VQE, mitigating the core obstacles that impede its practical implementation in the field of molecular quantum chemistry.

Figures (8)

• Figure 1: Variations in (a) energy error, (b) initial gradient magnitudes of newly added operators, (c) initial parameter magnitudes of newly added operators, and (d) final parameter magnitudes of all variational parameters in the ansatz with respect to iteration number in the ground-state simulation of the BeH2 molecule (R(Be-H)=2.6Å).
• Figure 2: (a--c) Energy error and (d--f) measurement cost as functions of iteration number on LiH, H2O, and NH3 with uniformly stretched bond lengths of 3.24 Å, 2.06 Å, and 1.6 Å, respectively.
• Figure 3: Evolution of energy error and measurement cost with iteration for H4 at different bond lengths.
• Figure 4: Evolution of energy error and measurement cost with iteration for LiH at different bond lengths.
• Figure 5: Evolution of energy error and measurement cost with iteration for HF at different bond lengths.