{
  "abstract": "Recent advances in coherent spin shuttling have made sparse semiconductor spin-qubit arrays an appealing solid-state platform to realize quantum processors 1–7 . The dynamic and long-range connectivity enabled by shuttling is also essential for many quantum error-correction schemes 8–10 . Here we demonstrate a silicon spin-qubit device comprising a shuttling bus for coherently transporting qubits that can interact at four isolated locations that we call bus stops. We dynamically populate the array and tune all single- and two-qubit operations using shuttling and quantum non-demolition spin measurements, without access to charge sensing in most of the device. We achieve universal control of the effective five-qubit processor and select the connectivity required to form a surface-code stabilizer plaquette that supports X - and Z -type parity checks up to weight four. We use the parity checks to generate multi-qubit entanglement between all qubit combinations in the array and report the genuine entanglement of a five-qubit Greenberger–Horne–Zeilinger state, constituting one of the largest such states constructed with gate-defined semiconductor spins. The protocols developed here lay the groundwork for modular calibration and operation of sparse spin-qubit arrays, and we highlight the feasibility of near-term quantum error-correction experiments with mobile spin qubits.",
  "abstract_shown": true,
  "affiliations": [
    "QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands",
    "Netherlands Organization for Applied Scientific Research (TNO), Delft, The Netherlands",
    "QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands. l.m.k.vandersypen@tudelft.nl"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 10,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Brennan Undseth",
      "orcid": "0000-0003-4445-9027"
    },
    {
      "affs": [
        0
      ],
      "name": "Nicola Meggiato",
      "orcid": "0000-0001-5374-3076"
    },
    {
      "affs": [
        0
      ],
      "name": "Yi-Hsien Wu",
      "orcid": "0009-0002-4137-989X"
    },
    {
      "affs": [
        0
      ],
      "name": "Sam R. Katiraee-Far"
    },
    {
      "affs": [
        1
      ],
      "name": "Larysa Tryputen"
    },
    {
      "affs": [
        0
      ],
      "name": "Sander L. de Snoo",
      "orcid": "0000-0003-4525-4023"
    },
    {
      "affs": [
        0
      ],
      "name": "Davide Degli Esposti",
      "orcid": "0000-0003-2275-8288"
    },
    {
      "affs": [
        0
      ],
      "name": "Giordano Scappucci",
      "orcid": "0000-0003-2512-0079"
    },
    {
      "affs": [
        0
      ],
      "name": "Eliška Greplová",
      "orcid": "0000-0003-3369-2544"
    },
    {
      "affs": [
        2
      ],
      "name": "Lieven M. K. Vandersypen",
      "orcid": "0000-0003-4346-7877"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8j6vkt2bagdm1.bib",
  "cited_by": 22,
  "doi": "10.1038/s41586-026-10766-3",
  "fulltext_url": null,
  "id": "8j6vkt2bagdm1",
  "issns": [
    "0028-0836",
    "1476-4687"
  ],
  "landing_url": "https://doi.org/10.1038/s41586-026-10766-3",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3104|Quantum and electron transport phenomena"
    ]
  ],
  "openalex": "W7171706912",
  "pdf_url": null,
  "pmcid": "PMC13421349",
  "pmid": "42527563",
  "published": "2026-07-29",
  "publisher": "Nature Portfolio",
  "ris": "https://research.draconitic.com/paper/8j6vkt2bagdm1.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T13:20:39Z",
      "native_id": "W7171706912",
      "source": "openalex",
      "url": "https://doi.org/10.1038/s41586-026-10766-3"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3104|Quantum and electron transport phenomena",
      "subfield": "quantum"
    }
  ],
  "title": "Weight-four parity checks in a spin-shuttling architecture",
  "title_text": "Weight-four parity checks in a spin-shuttling architecture",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:39Z",
  "url": "https://research.draconitic.com/paper/8j6vkt2bagdm1",
  "venue": "Nature",
  "versions": []
}