{
  "abstract": "We construct the first known fault-tolerant scheme for injecting states into quantum error-correcting codes with constant space and time overhead. That is, we construct a family of constant-rate quantum error-correcting codes for which a set of bare physical qubits can be injected, i.e. fault-tolerantly encoded, into a code block. Similarly, a code state can be ejected, i.e. fault-tolerantly decoded, back into bare physical qubits. We show that these injection and ejection procedures succeed under circuit-level locally stochastic noise, while incurring just a small constant probability of corrupting each qubit, which is unavoidable for bare physical qubits. We also show how to perform fault-tolerant error correction and code-state preparation under locally stochastic noise. All of our gadgets can be implemented with constant quantum circuit depth (i.e. are single-shot), and with a number of physical qubits growing linearly with the number of logical qubits, assuming the ability to run polynomial-sized noiseless classical circuits on the side. We construct our quantum codes by taking a high-dimensional hypergraph product of classical LDPC codes, which in turn are a simplified version of Spielman's linear-time encodable codes (STOC'95). As our resulting product codes are only resilient to physical errors occurring with non-uniform probabilities across qubits, we then show how to concatenate with inner codes of various sizes to obtain fault-tolerance against uniform noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39345",
  "author_total": 2,
  "authors": [
    {
      "name": "Louis Golowich"
    },
    {
      "name": "Venkatesan Guruswami"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ez5kjkwmsc1x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39345",
  "fulltext_url": null,
  "id": "7ez5kjkwmsc1x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39345",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215111368",
  "pdf_url": "https://arxiv.org/pdf/2609.39345",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ez5kjkwmsc1x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39345",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39345"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Constant-Overhead Injection into Quantum Codes",
  "title_text": "Constant-Overhead Injection into Quantum Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/7ez5kjkwmsc1x",
  "venue": "arXiv",
  "versions": []
}