{
  "abstract": "Realizing practical quantum computers requires quantum error correction, but the most widely implemented approach, the planar surface code, demands a substantial physical qubit overhead. Here, we demonstrate that partitioning quantum processors into manageable, flat modules with non-local inter-module connections provides a natural solution. By wiring sparse, static boundary connections between Euclidean planar modules, we construct modular hyperbolic surface and color codes, based on new families of semi-hyperbolic codes. Using modular syndrome extraction circuits and efficient neural network and matching decoders, our circuit-level simulations show that this modular memory design can reduce the physical qubit overhead by tenfold or more compared to the surface code, even under elevated inter-module seam error rates. Projecting to larger system sizes, we find modular codes with encoding rate $k/n=1/16$ and distance $d\\geq 22$, exceeding both the rate and distance of the $[[288,12,18]]$ two-gross bivariate bicycle code while using mostly nearest-neighbor gates within planar modules, and implying an over $30\\times$ overhead reduction relative to surface codes. We develop fault-tolerant walking circuits for implementing logic via code automorphisms, which we co-design with low-weight, highly symmetrical logical bases and a modular extractor system that is $\\approx 4.5\\times$ smaller than the code itself. Combining these methods, our modular memory can be used as dense storage in a universal fault-tolerant architecture, unlocking the efficiency of high-rate codes without sacrificing the fabrication advantages of planar modules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03682",
  "author_total": 14,
  "authors": [
    {
      "name": "Oscar Higgott"
    },
    {
      "name": "Hasan Sayginel"
    },
    {
      "name": "Francisco J. H. Heras"
    },
    {
      "name": "Zhiyang He"
    },
    {
      "name": "Tomas Jochym-O'Connor"
    },
    {
      "name": "Andrew W. Senior"
    },
    {
      "name": "Lei M. Zhang"
    },
    {
      "name": "Thomas Edlich"
    },
    {
      "name": "James S. Spencer"
    },
    {
      "name": "Matt McEwen"
    },
    {
      "name": "Craig Gidney"
    },
    {
      "name": "Johannes Bausch"
    },
    {
      "name": "Pushmeet Kohli"
    },
    {
      "name": "Hartmut Neven"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/104k7j8w21tgt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03682",
  "fulltext_url": null,
  "id": "104k7j8w21tgt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03682",
  "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": "W7220464812",
  "pdf_url": "https://arxiv.org/pdf/2610.03682",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/104k7j8w21tgt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03682",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03682"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Low-Overhead Quantum Error Correction with Boundary-Connected Planar Modules",
  "title_text": "Low-Overhead Quantum Error Correction with Boundary-Connected Planar Modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/104k7j8w21tgt",
  "venue": "arXiv",
  "versions": []
}