{
  "abstract": "We explore a continuous-time quantum walk starting at a single vertex on the discrete path and cycle with a cubic nonlinearity. Such nonlinearities arise in Bose-Einstein condensates described by the Gross-Pitaevskii equation or by nonlinear optical waveguide arrays. When the nonlinearity is sufficiently strong, the walker remains localized at its initial vertex, a phenomenon known as self-trapping. This contrasts with linear quantum walks, which are known for spreading quickly in one dimension. While self-trapping has been known numerically, we introduce an analytical method that proves self-trapping and yields a quantitative relationship between the nonlinearity coefficient and the trapping probability. We propose that this trapping can be used for timing in quantum state transfer, where a qubit is held at a node until it is ready to be transferred, and it can also be held again at the receiving node. This scheme can also be interpreted as a form of quantum memory, with the trap and transfer corresponding to the storage and release of quantum information.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys. Scr. 101, 365101 (2026)",
  "arxiv": "2605.20464",
  "author_total": 2,
  "authors": [
    {
      "name": "Yujia Shi"
    },
    {
      "name": "Thomas G. Wong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5bwv6x6gsqe2y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.20464",
  "fulltext_url": null,
  "id": "5bwv6x6gsqe2y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.20464",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2605.20464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5bwv6x6gsqe2y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "2605.20464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.20464"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Self-Trapping Bounds for Continuous-Time Nonlinear Quantum Walks on Path and Cycle Graphs",
  "title_text": "Self-Trapping Bounds for Continuous-Time Nonlinear Quantum Walks on Path and Cycle Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:14Z",
  "url": "https://research.draconitic.com/paper/5bwv6x6gsqe2y",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1088/1402-4896/aea02d",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}