{
  "abstract": "We prove a fault-tolerance theorem for quantum computation against adversarial noise. For every quantum circuit on $\\bar{N}$ logical qudits of depth $\\bar{T}$, we construct a fault-tolerant circuit on $N=\\text{poly}(\\bar{N})$ physical qudits of depth $\\bar{T}\\cdot\\bar{N}^{o(1)}$, which is robust against an adversary who may arbitrarily choose and corrupt an almost-linear number $N^{1-o(1)}$ of physical qudits at each time step. This robustness significantly improves upon prior fault-tolerance theorems, which assumed corruptions were either local and stochastic, or else only act on a polynomially vanishing fraction of qudits. Our fault-tolerance scheme addresses a key bottleneck towards constructing quantum PCPs via the circuit-to-Hamiltonian mapping of Anshu, Breuckmann, and Nguyen (STOC'24). More fundamentally, our result demonstrates that fault-tolerant quantum computation remains possible under noise models that are global, worst-case, and non-Markovian over the full duration of the computation, directly countering concerns that correlated noise could fundamentally undermine quantum fault tolerance. Our construction is based on a new family of subsystem product codes we develop, which have large dimension and distance along with low-weight parity-checks, and which support transversal non-Clifford gates. We show how to perform single-shot fault-tolerant error correction on these codes using a Floquet-like procedure based on the local testability of classical tensor codes. We then obtain a universal fault-tolerance scheme using repeated code switching in a hypercubic qudit architecture. Finally, we recursively compose our scheme with itself to reduce an initially exponential qudit dimension down to a constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.16857",
  "author_total": 3,
  "authors": [
    {
      "name": "Nikolas P. Breuckmann"
    },
    {
      "name": "Louis Golowich"
    },
    {
      "name": "Umesh Vazirani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mvwmtk7sz2a3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.16857",
  "fulltext_url": null,
  "id": "2mvwmtk7sz2a3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.16857",
  "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.CC"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7203698659",
  "pdf_url": "https://arxiv.org/pdf/2608.16857",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mvwmtk7sz2a3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2608.16857",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.16857"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fault-Tolerant Quantum Computation with Adversarial Errors",
  "title_text": "Fault-Tolerant Quantum Computation with Adversarial Errors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/2mvwmtk7sz2a3",
  "venue": "arXiv",
  "versions": []
}