{
  "abstract": "Fault-tolerant compilation can disperse high-level structure: schedules split an accumulated phase across rounds, gate synthesis replaces an angle by a Clifford+$T$ word, and randomized compiling spreads rotations over sign-randomized fragments. They preserve the computation but change how cheaply a downstream compiler can recover the aggregate phase data. We formalize this representation-dependent recoverability by charging two channels: output committed before the suffix arrives, and a serialized restart state crossing the cut. For an $r$-round accumulation of a commuting layer with $m$ generators at accuracy $ε$ ($K_ε=Θ(1/ε)$), any $p$-pass compiler correct on every valid stream with failure probability at most $δ$ obeys $\\overline{A}_p+(2p-1)S\\geq(1-δ)m\\log_2 K_ε-h_2(δ)$, where $\\overline{A}_p$ is committed output and $S$ is the crossing-state cap. The bound covers compile-time randomized compiling; a memory-capped block compiler attains it within a constant factor, and direct semantic aggregation reaches compact output with logarithmic state. The two channels are not always interchangeable. A compiler whose committed prefix is executed at the cut pays a toll the state channel never pays: the entropy $\\log_2\\binom{m}{k}$ of the mask naming which $k$ coordinates it commits early. Compilers that defer or buffer pay none of it. We prove both directions and, with instrumented compilers under a preregistered protocol, measure a per-generator toll matching $\\log_2\\binom{m}{k}/k$ that vanishes for a public mask and a buffered control. Under a disclosed fixed-total-error Clifford+$T$ and surface-code model, a materialize-first pipeline costs orders of magnitude more logical $T$ states and spacetime volume than a semantic-first one. Phase semantics should therefore be preserved until aggregation whenever the interface permits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29210",
  "author_total": 3,
  "authors": [
    {
      "name": "Jinze Yang"
    },
    {
      "name": "Yangyang Li"
    },
    {
      "name": "Xiu-Hao Deng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eka2m8kw8c408.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29210",
  "fulltext_url": null,
  "id": "eka2m8kw8c408",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29210",
  "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": "W7214392721",
  "pdf_url": "https://arxiv.org/pdf/2609.29210",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eka2m8kw8c408.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.29210",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29210"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Representation-Dependent Recoverability in Quantum Compilation",
  "title_text": "Representation-Dependent Recoverability in Quantum Compilation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/eka2m8kw8c408",
  "venue": "arXiv",
  "versions": []
}