{
  "abstract": "We investigate ancilla-free linear combination of unitaries (LCU) as a framework for approximating complex quantum circuits. This is particularly effective for quantum optimization algorithms, where candidate solutions can be evaluated classically and the task is to sample high-quality bitstrings rather than reproduce the full output distribution. We show that Fourier-based LCU constructions efficiently decompose broad classes of diagonal and non-diagonal unitaries, replacing highly connected qubit interactions with single-qubit gate layers or significantly simpler structures at the cost of a polynomial sampling overhead. Applied to algorithms such as QAOA, this yields efficient, hardware-friendly decompositions of, for instance, cardinality-constraint penalties and the fully connected XY-mixer, while maintaining rigorous performance guarantees compared to fully coherent implementations. Furthermore, we establish a formal connection between Fourier-based quantum penalties and Lagrangian relaxation, offering a unified perspective on constraint handling. We validate our approach using exact statevector simulations of 12-qubit circuits and large-scale experiments on 106 superconducting qubits. Our results illustrate how approximate sampling via an LCU systematically trades circuit complexity for sampling overhead, extending the practical reach of near-term quantum optimization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.18985",
  "author_total": 3,
  "authors": [
    {
      "name": "Almudena Carrera Vazquez"
    },
    {
      "name": "Daniel J. Egger"
    },
    {
      "name": "Stefan Woerner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wed2bh0ged8h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.18985",
  "fulltext_url": null,
  "id": "2wed2bh0ged8h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.18985",
  "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": "W7161767253",
  "pdf_url": "https://arxiv.org/pdf/2605.18985",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wed2bh0ged8h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2605.18985",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.18985"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Efficient Fourier-Based Linear Combination of Unitaries and Applications in Quantum Optimization",
  "title_text": "Efficient Fourier-Based Linear Combination of Unitaries and Applications in Quantum Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:31Z",
  "url": "https://research.draconitic.com/paper/2wed2bh0ged8h",
  "venue": "arXiv",
  "versions": []
}