Reducing quantum measurements in qubit-based overlapping grouping methods for quantum energy estimation through better initializations

Abstract:The measurement cost for estimating expectation values of Hamiltonians is a central bottleneck in variational quantum algorithms. Grouping strategies significantly reduce this cost, with overlapping techniques being the state of the art in the field. Overlapping grouping methods require i) a non-overlapping grouping of the Hamiltonian, typically obtained from the Sorted Insertion (SI) algorithm as initialization, and ii) the construction of covariance dictionaries from approximate wavefunctions to guide the optimization. It was recently shown that different initializations can potentially reduce measurement costs for overlapping methods. Motivated by these findings, we introduce variance-aware SI (VarSI), a family of covariance-informed non-overlapping Pauli grouping heuristics to reduce measurement counts. VarSI grouping leverages the covariance dictionaries, already required by overlapping methods, to construct better non-overlapping groups. We propose three variants: a global greedy grouping insertion rule, a variance-informed SI analog, and a local refinement step initialized from SI or our variance-informed variant. We showcase the use of groupings generated by our VarSI heuristic algorithms to initialize overlapping methods using the iterative coefficient-splitting (ICS) algorithm. Molecular benchmarks with 130 Hamiltonians demonstrate consistent, non-overlapping measurement improvements over SI of 38\% and enhanced downstream ICS results when initialized from VarSI groups. We find that the initializations considered here achieve up to 70\% measurement reductions for ICS, compared to the standard SI initialization with mean reductions of 9--15.3\% depending on qubit mappings and covariance dictionaries used. These results show that non-overlapping grouping remains a consequential design step even when the final estimator uses overlapping fragments.

Main paper: 8 pages, 1 figure, 2 tables. Supplementary Material: Contact authors or check v1: 22 pages, 4 figures, 5 tables

arXiv:2607.02794 [quant-ph]

(or arXiv:2607.02794v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.02794 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.