{
  "abstract": "We investigate the construction of unitary \\(1\\)-designs and two-photon designs on programmable linear-optical interferometers. Using the frame-potential loss as the optimization objective, we identify architectures that reproduce the relevant Haar moments with considerably fewer programmable phase shifters than required for universal linear optics. For unitary \\(1\\)-designs, we provide an exact construction and prove that the minimum number of programmable phase shifters within the considered layered architecture is \\(2(d-1)\\), where \\(d\\) is the number of optical modes. Numerical optimization confirms this parameter count over the tested range of dimensions. For two-photon designs, defined by first-moment matching in the symmetric two-photon representation of \\(U(d)\\), we numerically investigate the resources required to achieve prescribed approximation thresholds. We benchmark the resulting ensembles using single- and two-photon transition probabilities and average channel fidelities. Furthermore, we develop a protocol for estimating the total photon number of a multiphoton Fock state using a single monitored output mode and derive the corresponding Haar-averaged photon-count moments. Our findings demonstrate that shallow interferometers can reproduce Haar-averaged observables with reduced hardware resources, while photon-number fluctuations provide a more stringent test of approximate two-photon designs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12646",
  "author_total": 3,
  "authors": [
    {
      "name": "Robert A. Grinshtein"
    },
    {
      "name": "Ivan V. Dyakonov"
    },
    {
      "name": "Stanislav S. Straupe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2nnzkwz7gh25.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12646",
  "fulltext_url": null,
  "id": "f2nnzkwz7gh25",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12646",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.optics"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7221521225",
  "pdf_url": "https://arxiv.org/pdf/2610.12646",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2nnzkwz7gh25.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.12646",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12646"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal linear-optical interferometers for unitary t-designs in a multi-photon Fock space",
  "title_text": "Optimal linear-optical interferometers for unitary t-designs in a multi-photon Fock space",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:15Z",
  "url": "https://research.draconitic.com/paper/f2nnzkwz7gh25",
  "venue": "arXiv",
  "versions": []
}