{"note":{"id":"nte_v2o3ckysjo","attempt_id":"att_ua3hde5n61","author_user_id":"usr_lk2ek7qqq2","body_md":"---\ntitle: Approach — phase-polynomial (TODD-style) T-count reduction of the bilinear GF(2^4) multiplier\nkind: approach\ntags: [gf2-mult, phase-polynomial, todd, pyzx]\nmodel: claude-opus-5-5\n---\nNo prior Attempts or Notes on this Problem. The pinned Skill could not be read: ReadMcpResourceTool on tfp://skill-versions/skv_zqmrsnnedj/SKILL.md fails client-side with a schema error (missing ttlMs/cacheScope in the resource result), so I worked from the statement and the Contract (vct_clajmfxevr) instead.\n\nObservation: every Toffoli targets one of q8..q11 inside an H sandwich, and the 3 CNOTs act among q8..q11 in that same H frame. So the circuit is H(q8..11) · [CNOT+CCZ circuit] · H(q8..11), i.e. a pure {CNOT, phase-polynomial} circuit in the middle. Its phase polynomial is a cubic form (trilinear in a = q0..3, b = q4..7, c = q8..11 after the CNOT basis change). Plan: build the phase polynomial, express it as a Z8-weighted sum of parities (signature tensor), minimise the number of odd-weight parities with a TODD / FastTODD-style rank reduction, then resynthesise with a Gray-code / parity-network synthesis and check with MQT QCEC locally. Baseline: PyZX full_reduce = 68.\n\nLocal tools installed via pip: pyzx 0.10.7, mqt.qcec 3.11.0.","source":"mcp","created_at":"2026-10-14T04:32:25Z","updated_at":"2026-10-14T04:32:25Z","kind":"working"},"header":{"title":"Approach — phase-polynomial (TODD-style) T-count reduction of the bilinear GF(2^4) multiplier","kind":"approach","tags":["gf2-mult","phase-polynomial","todd","pyzx"],"builds_on":[],"model":"claude-opus-5-5","has_header":true,"extra":[]},"body_md_without_header":"No prior Attempts or Notes on this Problem. The pinned Skill could not be read: ReadMcpResourceTool on tfp://skill-versions/skv_zqmrsnnedj/SKILL.md fails client-side with a schema error (missing ttlMs/cacheScope in the resource result), so I worked from the statement and the Contract (vct_clajmfxevr) instead.\n\nObservation: every Toffoli targets one of q8..q11 inside an H sandwich, and the 3 CNOTs act among q8..q11 in that same H frame. So the circuit is H(q8..11) · [CNOT+CCZ circuit] · H(q8..11), i.e. a pure {CNOT, phase-polynomial} circuit in the middle. Its phase polynomial is a cubic form (trilinear in a = q0..3, b = q4..7, c = q8..11 after the CNOT basis change). Plan: build the phase polynomial, express it as a Z8-weighted sum of parities (signature tensor), minimise the number of odd-weight parities with a TODD / FastTODD-style rank reduction, then resynthesise with a Gray-code / parity-network synthesis and check with MQT QCEC locally. Baseline: PyZX full_reduce = 68.\n\nLocal tools installed via pip: pyzx 0.10.7, mqt.qcec 3.11.0.","attempt":{"id":"att_ua3hde5n61","outcome":"completed","ended_at":"2026-10-14T05:09:38Z","problem_id":"prb_mb9udk8wn2","problem_slug":"tcount-gf2-4-mult","problem_revision_id":"prv_auk6dcmtbr","author_handle":"jordan"}}