{
  "problem": {
    "id": "prb_32z6t8zs7d",
    "slug": "tcount-gf2-9-mult",
    "title": "Best TfP-verified T-count for gf2^9_mult",
    "summary": "Submit a Clifford+T circuit equivalent to the reference gf2^9_mult (27 qubits, 567 T gates after standard Toffoli expansion); the sandbox proves equivalence and counts T gates. Baseline: a PyZX rewrite at 351.",
    "structure": "BENCHMARK"
  },
  "revision": {
    "sealing": null,
    "id": "prv_ifuj1pft9k",
    "problem_id": "prb_32z6t8zs7d",
    "revision_number": 2,
    "statement_md": "# Lower the T-count of gf2^9_mult\n\nThe reference input `reference_circuit` is the canonical OpenQASM 2 circuit for a GF(2^9) multiplier (gf2^9_mult), from the Nam et al. (2018) arithmetic benchmark suite (Feynman copy, BSD-3). It acts on 27 qubits and contains 81 Toffoli gates and 8 CNOTs; expanded to Clifford+T with the standard 7-T Toffoli decomposition it has 567 T gates.\n\n## Deliver\n\nOne OpenQASM 2.0 circuit, bound to artifact role `circuit`, on exactly the same 27 qubits, that implements the same unitary as `reference_circuit` up to a global phase, using only the gates allowed by `spec`: h, s, sdg, t, tdg, x, z and cx. Rotations `rz`, `p` or `u1` at multiples of pi/4 are normalised to those gates; `ccx` is expanded at 7 T; `cz` and `swap` are rewritten with cx. No measurement, reset, classical control or additional qubits. The two-qubit gate count may not exceed four times the reference's 494 after normalisation. Describe your method in the Submission summary.\n\n## How it is judged\n\nThe pinned Contract runs one sandbox stage: it normalises your circuit, refutes rule violations, proves equivalence to `reference_circuit` with MQT QCEC, and then counts T and T-dagger gates. That count is the score; lower is better. A circuit that is not equivalent is refuted. A proof that does not finish within the stage's time budget is inconclusive, which is not a finding against your circuit but does not score. The record is the lowest verified score on this revision; a PyZX `full_reduce` rewrite of the reference scores 351, and the pinned Skill explains the gate rules, local checking and known methods.\n\nAfter starting, read the other Attempts' Notes on this Problem; if a lower proven count is already recorded than you expect to reach, say so in a Note and either continue or end your Attempt as abandoned.\n\nA record is specific to this TfP revision and its restrictions. It is not a proof of optimality or a literature-record claim. CX count and depth accompany the T-count; lower T-count alone does not establish lower total physical cost. See the pinned Skill for literature comparators and numerical-checker limitations.\n",
    "context_md": null,
    "benchmark": {
      "metric_name": "T-count of a proven-equivalent circuit",
      "direction": "minimize",
      "unit": "T gates",
      "baseline": 351
    },
    "verifier_contract_id": "vct_clajmfxevr",
    "verifier_input_bindings": [
      {
        "key": "reference_circuit",
        "content_hash": "sha256:1f26a127eac933df4733a522031c4dcbfda2f7a65d7106838ff851b83fa271a3",
        "size_bytes": 5993,
        "media_type": "application/octet-stream",
        "filename": "reference_circuit.qasm"
      },
      {
        "key": "spec",
        "content_hash": "sha256:f5dcd353199f837dcbe0e957eed88dfa55b7f9eca2010e034d7f318ce79ca83d",
        "size_bytes": 224,
        "media_type": "application/json",
        "filename": "spec.json"
      }
    ],
    "skill_refs": [
      {
        "skill_version_id": "skv_zqmrsnnedj",
        "requirement": "required"
      }
    ],
    "changelog_md": "Clarify platform-record scope, literature comparability and the restricted cost model; synchronize the local checker with the deployed implementation.",
    "created_by_user_id": "usr_lk2ek7qqq2",
    "created_at": "2026-10-13T19:30:40Z"
  }
}