{
  "abstract": "In Fault-Tolerant Quantum Computing (FTQC) using surface codes, reducing $T$-count is critical for efficient computation due to the high cost of $T$-state distillation. Probabilistic Quantum Circuit with Fallback (PQF) synthesis significantly lowers $T$-counts compared to standard protocols like Gridsynth, but introduces high circuit dynamism through extra gates inserted at runtime. This dynamism invalidates static compile-time routing, as these new $T$ gates require dynamic lattice surgery routing to establish non-intersecting ancilla paths to $T$-state factories while minimizing total execution time. To address this, we introduce $\\text{R}^2$-PQF, a Runtime Routing protocol for PQF-synthesized quantum circuits. $\\text{R}^2$-PQF dynamically routes gates layer-by-layer, computing paths during the execution of the previous logical timestep. To satisfy the strict computational window of $\\sim t_{lattice\\_surgery} + t_{reaction}$ and non-intersectionality constraints, we implement a Wavefront Breadth-First Search (W-BFS) and synthesise it on a 500MHz FPGA and 2 GHz ASIC. For a clock cycle of 2GHz, we achieve a median logical time-step of $1.51 μs$ for a 300 qubit Ising Hamiltonian circuit, demonstrating that $\\text{R}^2$-PQF successfully resolves the vast majority of paths (with rare exceptions) within the execution window and enables the $T$-count benefits of PQF without latency penalties. Compared to a baseline stalling-based solution (the only no-runtime-recomputation solution), $\\text{R}^2$-PQF speeds up circuit execution by $1.34\\times$ on average and up to $1.76 \\times$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04075",
  "author_total": 6,
  "authors": [
    {
      "name": "Siddharth Dangwal"
    },
    {
      "name": "Christopher Kang"
    },
    {
      "name": "Jad Habhab"
    },
    {
      "name": "Ritvik Sharma"
    },
    {
      "name": "Frederic T. Chong"
    },
    {
      "name": "Gokul Subramanian Ravi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/19st78b3s19cs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04075",
  "fulltext_url": null,
  "id": "19st78b3s19cs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04075",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04075",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/19st78b3s19cs.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.04075",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04075"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Runtime Compilation for Quantum Circuits with PQF-Enabled $R_z$ Synthesis",
  "title_text": "Runtime Compilation for Quantum Circuits with PQF-Enabled R_z Synthesis",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:25Z",
  "url": "https://research.draconitic.com/paper/19st78b3s19cs",
  "venue": "arXiv",
  "versions": []
}