{
  "abstract": "In this paper, we analyze state transfer in quantum walks by using combinatorial methods. We generalize perfect state transfer in two-reflection discrete-time quantum walks to a notion that we call peak state transfer; we define peak state transfer as the highest state transfer that can be achieved between an initial and a target state under unitary evolution, even when perfect state transfer is unattainable. We give a spectral characterization of peak state transfer that allows us to fully characterize peak state transfer in the arc-reversal (Grover) walk on various families of graphs, including strongly regular graphs and incidence graphs of block designs (assuming that the walk starts at a point of the design). In addition, we provide many examples of peak state transfer, including an infinite family where the amount of peak state transfer tends to $1$ as the number of vertices grows. We further demonstrate that peak state transfer properties extend to infinite families of graphs generated by vertex blow-ups, and we characterize periodicity in the vertex-face walk on toroidal grids. In our analysis, we make extensive use of the spectral decomposition of a matrix that is obtained by projecting the transition matrix down onto a subspace. Though we are motivated by a problem in quantum computing, we identify several open problems that are purely combinatorial, arising from the spectral conditions required for peak state transfer in discrete-time quantum walks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Krystal Guo"
    },
    {
      "name": "Vincent Schmeits"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2c71462rn9qjq.bib",
  "cited_by": 1,
  "doi": "10.37236/13764",
  "fulltext_url": null,
  "id": "2c71462rn9qjq",
  "issns": [
    "1077-8926"
  ],
  "landing_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p4",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W4404389795",
  "pdf_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i4p4/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": "The Electronic Journal of Combinatorics",
  "ris": "https://research.draconitic.com/paper/2c71462rn9qjq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:24Z",
      "native_id": "10.37236/13764",
      "source": "crossref",
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p4"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:1077-8926",
      "subfield": "combinatorics"
    }
  ],
  "title": "State Transfer in Discrete-Time Quantum Walks via Projected Transition Matrices",
  "title_text": "State Transfer in Discrete-Time Quantum Walks via Projected Transition Matrices",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:24Z",
  "url": "https://research.draconitic.com/paper/2c71462rn9qjq",
  "venue": "The Electronic Journal of Combinatorics",
  "versions": []
}