{
  "abstract": "Pseudorandom error-correcting codes (PRCs), introduced by Christ and Gunn [CRYPTO 2024], are classical error-correcting codes whose codewords are computationally indistinguishable from uniformly random strings. We initiate the study of quantum analogues of PRCs. We define quantum pseudorandom error-correcting codes (QPRCs). Assuming that Learning Parity with Noise (LPN) is hard for $2^{O(\\sqrt{n})}$-time quantum algorithms, we construct QPRCs whose encodings are indistinguishable from Haar-random isometries. We call these pseudorandom isometric error-correcting codes (PRICs), and our construction is robust to all $o(n \\frac{\\log \\log n}{\\log n})$-local quantum noise, where $n$ is the number of physical qubits. Under the same assumption, we also construct QPRCs whose encodings are indistinguishable from the completely depolarizing channel and that are robust to all $αn$-local quantum noise for some constant $α>0$. The latter QPRCs give a direct quantum analogue of classical PRCs. To construct PRICs, we develop two technical ingredients of independent interest. First, we introduce a new classical cryptographic primitive which we call pseudorandom functional error-correcting codes (PRFCs) and construct them under the same LPN assumption. Second, we develop a new efficient decoding procedure within the codeword-stabilized (CWS) framework introduced in [Cross, Smith, Smolin, and Zeng, IEEE ISIT 2008], which is a generic framework for constructing quantum error-correcting codes by combining (possibly nonlinear) classical error-correcting codes and graphs. This resolves the open problem of finding a general method for efficiently decoding such CWS codes based on nonlinear classical codes, raised in [Li, Dumer, Grassl, and Pryadko, Physical Review A 2010].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38986",
  "author_total": 2,
  "authors": [
    {
      "name": "Min-Hsiu Hsieh"
    },
    {
      "name": "Shogo Yamada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/373qxmhe5b4bw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38986",
  "fulltext_url": null,
  "id": "373qxmhe5b4bw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38986",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215079770",
  "pdf_url": "https://arxiv.org/pdf/2609.38986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/373qxmhe5b4bw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38986"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Pseudorandom Error-Correcting Codes",
  "title_text": "Quantum Pseudorandom Error-Correcting Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/373qxmhe5b4bw",
  "venue": "arXiv",
  "versions": []
}