{
  "abstract": "Programmable photonic integrated circuits are emerging as increasingly large and versatile interferometric processors operating at room temperature. However, their native operations are linear, while many computational tasks require nonlinear input-output transformations that typically rely on nonlinear optical materials or resonant devices. Here, we establish a direct mapping between quantum signal processing (QSP) and the native two-mode operations of programmable interferometric photonic integrated circuits, showing that the $SU(2)$ structure required by QSP can be realized through programmable phase control and mode mixing. We experimentally demonstrate this correspondence using dual-rail single-photon encoding on a 24-mode programmable photonic integrated circuit, realizing QSP sequences up to depth $L=11$ and synthesizing STEP, ReLU and SELU functions through programmable phase control. The optical transformation remains linear, while repeated encoding of the input variable and coherent interference produce a nonlinear dependence of the output probabilities on the encoded variable. Across all accessible circuit depths, the measured responses follow the programmed QSP transformations, with hardware-induced mean squared errors between $10^{-3}$ and $10^{-2}$, all remaining below the intrinsic finite-depth approximation error. These results establish an algorithm-to-hardware mapping of QSP on programmable photonic processors. They also demonstrate an algorithmic route to programmable nonlinear functions of encoded variables on linear photonic hardware.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14153",
  "author_total": 4,
  "authors": [
    {
      "name": "Elaheh Karooby"
    },
    {
      "name": "Masoud Hakimi Heris"
    },
    {
      "name": "Yuan Liu"
    },
    {
      "name": "Qing Gu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/133mr02ap6bxn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14153",
  "fulltext_url": null,
  "id": "133mr02ap6bxn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14153",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7213255786",
  "pdf_url": "https://arxiv.org/pdf/2609.14153",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/133mr02ap6bxn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14153",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14153"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Programmable nonlinear function synthesis on a photonic processor with quantum signal processing",
  "title_text": "Programmable nonlinear function synthesis on a photonic processor with quantum signal processing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/133mr02ap6bxn",
  "venue": "arXiv",
  "versions": []
}