{
  "abstract": "Repeated measurements can dominate the resources required for quantum energy estimation, making the choice of which Pauli observables to measure together a central optimization problem for variational quantum algorithms. We formulate fully commuting measurement grouping as a classical binary optimization problem based on clique selection and construct non-overlapping groups using mixed-integer linear programming (MILP). For a benchmark of molecular Hamiltonians, groupings optimized with approximate covariances reduce the non-overlapping measurement requirement $\\varepsilon^2M$ by $51.8\\%$ on average relative to sorted insertion (SI). Using the MILP groups to initialize iterative coefficient splitting (ICS), denoted MILP-ICS, yields an average $24.3\\%$ reduction relative to ICS initialized from SI (SI-ICS). The optimized groups also transfer across nearby molecular geometries while preserving substantial measurement savings. We further introduce O-clique, which directly optimizes overlapping commuting supports through candidate-clique selection and coefficient profiles. Although O-clique provides only modest additional reductions beyond MILP-ICS, it reduces the measurement requirement by $27.3\\%$ on average relative to SI-ICS with 100 iterations, despite using only five final coefficient refinement iterations, indicating improved support quality. Finally, we extend the comparison to Fermi--Hubbard, Kitaev--Heisenberg--$Γ$, and XYZ lattice Hamiltonians, where MILP-based groupings substantially outperform the corresponding SI-based strategies. Together, these results show that variance-informed optimization of measurement-group structure can substantially reduce sampling costs across molecular and lattice Hamiltonians, with optimized non-overlapping groups providing strong, transferable initializations and direct overlapping optimization offering further gains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10339",
  "author_total": 2,
  "authors": [
    {
      "name": "Isaac L. Huidobro-Meezs"
    },
    {
      "name": "Rodrigo A. Vargas-Hernández"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3901q2srqfemv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10339",
  "fulltext_url": null,
  "id": "3901q2srqfemv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10339",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220996506",
  "pdf_url": "https://arxiv.org/pdf/2610.10339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3901q2srqfemv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.10339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10339"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Binary Optimization of Measurement Groupings for Quantum Energy Estimation",
  "title_text": "Binary Optimization of Measurement Groupings for Quantum Energy Estimation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:37Z",
  "url": "https://research.draconitic.com/paper/3901q2srqfemv",
  "venue": "arXiv",
  "versions": []
}