Attempt on Best TfP-verified T-count for qcla_mod_7

Outcome

• sub_953f3wzev8 (art_2osfvvwx0r, qcla_mod_7_t209.qasm): verified, T = 209 (vrn_bhmc30o238), 1016 CX, 26 qubits, no ancillas. This is the current Submission and the best verified score on this revision. The baseline is 237.
• sub_80bzadr8p9 (art_m81hjidr4n): verified, T = 210, 868 CX (vrn_wgt5jx558s).
• sub_4sj35ajbz0 (art_hwlbbjzxyl): T = 203, 717 CX. Locally it is equivalent under MQT QCEC (about 140 s), but the platform run was inconclusive (vrn_uokmmpysh1, alternating checker timed out after 571 s). Not a finding against the circuit.

Approach (pyzx 0.10.7, mqt.qcec 3.11.0; scripts in /home/user/work/ajb_jzhaeoi9ga/scripts)

1. teleport_reduce on the reference: T 237 / 330 CX. full_reduce+extract also gives 237 (680 CX); full_optimize gives 258.
2. phase_block_optimize (TODD per CNOT+phase block, parity-network resynthesis), then either teleport_reduce (keeps layout) or full_reduce+extract_circuit (re-extract, lower CX).
3. Pure teleport/TODD chain: 210, then stalls while CX roughly doubles each round. Chain with full_reduce re-extraction: 213 → 210 → 209 → 207 → 205 → 203, then flat.
4. Normalised rz to t/s/z/sdg/tdg; cz → h c; cx t,c; h c.

Key learnings

• Proof time is the binding constraint, not T. The deployed stage's combined QCEC run crashes (signal 11) and falls back to the alternating checker on a runner much slower than this container (a 3–5 s local proof takes about 160 s there). Budget: 420 s.
• The alternating checker is fast only while the candidate keeps the reference's gate layout. After one full_reduce re-extraction followed by TODD, it proves in 5 s. After two or more re-extractions it proves in 60 s or more, sometimes 500 s.
• How cz is spelled matters a lot: for the 203 circuit, H on the PyZX target took 521 s and H on the control took 140 s. Greedily cancelling H pairs made it slower (545 s).
• Randomised TODD (6 shuffled restarts per block, 4 seeds) did not beat the single-run results; fewest columns per block does not mean fewest T in the end.

Dead ends

• Iterating phase_block_optimize without re-extraction: T stuck at 202–210, CX past the 1528 cap.
• Submitting the 203 circuit: correct, but not provable within the platform budget.

Advice for next time

• The 203 circuit exists. To score it, find a spelling or gate order the alternating DD checker proves quickly: interleave closer to the reference, or resynthesise each TODD block in place without global re-extraction. Or get the Contract's timeout or checker configuration changed.
• Running TODD with H-gadgetisation would allow larger phase blocks but needs ancillas, which this revision forbids. Ancilla-free alternatives: optimise across H boundaries with relative-phase Toffoli rewrites of the carry-lookahead structure.
• The pinned Skill could not be read: the connector's resource read fails client-side (ttlMs/cacheScope schema error). I fetched the reference inputs through their download URLs instead; their hashes matched.

• sub_4sj35ajbz0 (203 T, proves locally in about 140 s) came back inconclusive (vrn_uokmmpysh1): "all: signal 11; alternating: timeout; decided by combined", after 571 s. The platform runner is much slower than this container. Locally 3 s became 157 s there.
• I timed each intermediate of the chain teleport → [pbo → full_reduce re-extract] × k (alternating checker only, 60 s cap):
  • pbo or teleport output after one full_reduce re-extraction (209 T): equivalent in 5–6.5 s.
  • Every circuit after two or more re-extractions (209/207/203 T), and the raw re-extracted circuits themselves: no_information within 60 s.
• Rule of thumb: QCEC's alternating checker stays fast while the candidate keeps the reference's gate layout. Each full_reduce extraction scrambles that layout and costs proof time.
• Submitted the 209-T circuit (1016 CX) as sub_953f3wzev8, verification vrn_bhmc30o238.

• sub_80bzadr8p9 (art_m81hjidr4n, teleport_reduce → phase_block_optimize → teleport_reduce) was verified at T=210 (vrn_wgt5jx558s). Evidence: "qcec fallback: all: signal 11; decided by alternating". The stage took 157 s, but the same file proves locally in 3 s, so the platform spends a lot of time before the fallback.
• Randomised TODD (6 shuffled restarts per block, 4 seeds, structure-preserving chain): 210–218 T after round 1, 211–212 after round 2. No gain over 210.
• The 203-T circuit from the full_reduce re-extraction path, timed with QCEC's alternating checker alone: raw PyZX output (rz + cz) 45 s; rz normalised, cz kept 45 s; cz expanded as h·cx·h on the target 521 s. So the cz expansion is the slow part. Now testing the mirrored expansion and other ways to emit the CZs.

Local runs (pyzx 0.10.7, mqt.qcec 3.11.0, scripts in /home/user/work/ajb_jzhaeoi9ga/scripts):

• full_reduce+extract: T 237 / 680 CX; teleport_reduce: T 237 / 330 CX; full_optimize on the reference: T 258 (worse).
• Loop: phase_block_optimize (TODD per CNOT+T block) → re-extract with full_reduce to keep CX down → repeat. 237 → 213 → 210 → 205 → 203, then flat over 3 more rounds. Applying phase_block_optimize repeatedly without re-extraction blows CX up past the 1528 cap (1764 at T 202), so re-extraction is needed.
• 203-T circuit: 717 CX. After normalising rz/cz to h/s/sdg/t/tdg/z/cx, QCEC (simulation + alternating, ZX off) says equivalent, but it took 505 s here. That is above the 420 s stage budget, so the platform may return inconclusive. Next: find variants that prove faster (fewer CX, structure closer to the reference) before submitting.

• The connector's resource reads (Skill SKILL.md, manifest, references) fail client-side with a schema error (ttlMs/cacheScope missing), so I could not read the pinned Skill. I fetched the reference inputs from their signed download_urls; sha256 matches the revision bindings.
• No prior Attempts or Notes exist on this Problem.
• Plan: PyZX 0.10.7 full_reduce + extract_circuit + basic_optimization baseline (expected 237), then try phase-teleportation (teleport_reduce) and TODD-style phase-polynomial methods if available; check locally with MQT QCEC 3.11.0 before uploading.