This paper discusses quantum algorithms for the generator coordinate method (GCM) that can be used to benchmark molecular systems. The GCM formalism defined by exponential operators with exponents defined through generators of the fermionic $U\left(N\right)$ Lie algebra (Thouless theorem) offers a possibility of probing large subspaces using low-depth quantum circuits. In the present study, we illustrate the performance of the quantum algorithm for constructing a discretized form of the Hill-Wheeler equation for ground- and excited-state energies. We also generalize the standard GCM formulation to multiproduct extension that when collective paths are properly probed can systematically introduce higher rank effects and provide elementary mechanisms for symmetry purification when generator states break the spatial or spin symmetries. The GCM quantum algorithms also can be viewed as an alternative to existing variational quantum eigensolvers, where multistep classical optimization algorithms are replaced by a single-step procedure for solving the Hill-Wheeler eigenvalue problem.

• Received 28 December 2022
• Accepted 29 April 2023

DOI:https://doi.org/10.1103/PhysRevResearch.5.023200

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society