{
  "abstract": "The discrete Fourier transform (DFT) underpins many classical algorithms and is a fundamental unitary operator for quantum information processing. Implementing the $N$-dimensional DFT in photonic integrated circuits (PICs) is limited by the cascades of Mach-Zehnder interferometers that current architectures require. Here we propose bosonic Hamiltonians that realize the $N$-dimensional DFT through a single stage of multimode evolution, complemented only by phase shifters before and after the interaction region, in a geometry suited to 3D waveguides. Modeling the system as a graph, where edges correspond to couplings and the vertices are the waveguides, we obtain analytical solutions for complete graphs up to $N=6$ and numerical solutions up to $N=31$. For non-complete graphs, different propagation constants are required in the Hamiltonian. We report all solutions for $N\\leq 8$, partial exploration for $N=9$, and selected cases for $N=10$, together with three conjectures that guide the numerical search for $N \\geq 11$. These configurations circumvent the vanishing evanescent coupling strength imposed by the waveguide separation, and a closed-form sensitivity criterion selects those that are admissible as a waveguide layout and least sensitive to fabrication error. We also uncover the missing non-affine parameters of the $6$-dimensional DFT, and show that the scaling law for implementing the $N$-dimensional DFT with our building blocks is $\\mathcal{O}(N\\log\\log{N})$. This allows assembling the $2520$-dimensional DFT with only $2625$ interferometers, in contrast to the $\\approx 3\\times 10^6$ of Reck and Clements architectures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05644",
  "author_total": 7,
  "authors": [
    {
      "name": "Edgar Barriga"
    },
    {
      "name": "Camila Muñoz"
    },
    {
      "name": "Alejandro Muñoz"
    },
    {
      "name": "Santiago Rojas-Rojas"
    },
    {
      "name": "Pablo Solano"
    },
    {
      "name": "Carla Hermann-Avigliano"
    },
    {
      "name": "Aldo Delgado"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78s2nqb2grc11.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05644",
  "fulltext_url": null,
  "id": "78s2nqb2grc11",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05644",
  "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": "W7212042081",
  "pdf_url": "https://arxiv.org/pdf/2609.05644",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78s2nqb2grc11.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.05644",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05644"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "$N$-dimensional discrete Fourier transform via bosonic Hamiltonian",
  "title_text": "N-dimensional discrete Fourier transform via bosonic Hamiltonian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/78s2nqb2grc11",
  "venue": "arXiv",
  "versions": []
}