{
  "abstract": "Fault-tolerant quantum simulation requires compiling symmetry-preserving time evolutions into discrete gate sets. Standard Clifford+T synthesis can break continuous symmetries even when the target evolution preserves them, causing compiled simulations to lose essential features of the original system. We develop a fault-tolerant compilation framework that preserves SU(2) symmetry exactly. We characterize the number-theoretic obstruction preventing symmetry-preserving unitary Clifford+T circuits from approximating arbitrary SU(2)-symmetric evolutions and circumvent it using measurement and feed-forward. The resulting synthesis confines compilation errors to the symmetry-preserving operator algebra rather than introducing symmetry-breaking perturbations. We demonstrate the algorithm by simulating transport in the one-dimensional Heisenberg model. At a lower matched T-count, for instance, 54 T gates per two-site Trotter step, standard synthesis yields an incorrect transport exponent, whereas our symmetry-preserving compilation reproduces the expected exponent for the same expected T-count. If instead each approach is allocated whatever resources are necessary to estimate this exponent to the same accuracy, our construction reduces the T-count by approximately a factor of five. We further extend the framework to gauge symmetries in lattice gauge theories and to particle-number and spin symmetries in fermionic models relevant to quantum chemistry and the Fermi-Hubbard model. These results show that symmetry-preserving fault-tolerant compilation can qualitatively change the effects of synthesis error while substantially reducing the resources required for quantum simulation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03624",
  "author_total": 6,
  "authors": [
    {
      "name": "Maryam Mudassar"
    },
    {
      "name": "Zhi-Yuan Wei"
    },
    {
      "name": "Alexander Schuckert"
    },
    {
      "name": "Michael J. Lawler"
    },
    {
      "name": "Michael J. Gullans"
    },
    {
      "name": "Daniel Gottesman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/edvg8320zqgf7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03624",
  "fulltext_url": null,
  "id": "edvg8320zqgf7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03624",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220394517",
  "pdf_url": "https://arxiv.org/pdf/2610.03624",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/edvg8320zqgf7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03624",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03624"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Symmetry-preserving quantum compilation",
  "title_text": "Symmetry-preserving quantum compilation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/edvg8320zqgf7",
  "venue": "arXiv",
  "versions": []
}