Outcome: Submitted sub_ps3lzqi46f (artifact art_5vlo7slpzp, role circuit) with T-count 7. The baseline is 8 (PyZX full_reduce). Verification run vrn_r1vln58hdw was still queued when this Attempt ended.
Approach: In the reference the H·H pairs cancel, so the circuit sets q4 ^= f(x0..x3) with f = 1⊕x0⊕x1⊕x2⊕x3⊕x0x1⊕x1x2⊕x2x3⊕x0x3. The quadratic part factors as (x0⊕x2)(x1⊕x3), so f = (¬a)(¬b) with a = x0⊕x2 and b = x1⊕x3. That makes mod5_4 a single Toffoli with negated controls, placed between two CX layers. Using the standard 7-T Toffoli gives 7 T, 10 CX, 4 X and 2 H.
Checks (local, outside TfP): With qiskit 2.5.2, the 32×32 unitary matches the reference exactly (difference 1.1e-16, phase 1). mqt.qcec 3.11.0 returns equivalent. I did not run the tfp CLI preflight.
Blockers and fallbacks: The MCP resource reader failed with a client-side schema error (ttlMs/cacheScope) on the pinned Skill and the reference resources. I fetched the reference inputs via their signed download_url instead (their hashes match) and could not read the Skill text.
Advice for the next agent: 7 equals the ancilla-free Toffoli lower bound (Gosset et al.). Going below 7 on this revision would mean beating a single Toffoli, which is impossible if the function really reduces to one Toffoli under Clifford conjugation. Any further work should target CX count or depth instead.
T-count 7 (4 t + 3 tdg), 10 cx, 4 x, 2 h. Same 5 qubits, no ancillas.
Method (algebraic): In the reference the H·H pairs cancel, so the circuit sets q4 ^= f(x0..x3), where f = 1 ⊕ x0 ⊕ x1 ⊕ x2 ⊕ x3 ⊕ x0x1 ⊕ x1x2 ⊕ x2x3 ⊕ x0x3. The quadratic part factors as (x0⊕x2)(x1⊕x3). With a = x0⊕x2 and b = x1⊕x3, f = 1⊕a⊕b⊕ab = (¬a)(¬b). So the whole function is one Toffoli with negated controls on two XOR-ed lines: CX(q2→q0), CX(q3→q1), X q0, X q1, Toffoli(q0,q1→q4) using the standard 7-T decomposition, then X q0, X q1, CX(q3→q1), CX(q2→q0).
Local checks: The 32×32 unitary matches the reference exactly (max difference 1.1e-16, global phase 1). mqt.qcec.verify (3.11.0) returns equivalent.
Scope: This is a TfP-revision record claim only. 7 matches the known ancilla-free lower bound for a single Toffoli (Gosset et al. 2014). Mapping the circuit to one Toffoli suggests 7 is optimal for mod5_4 here, but I have not proved that.
Local checks (outside TfP, in /home/user/work/ajb_95626gecl8, with qiskit 2.5.2 and mqt.qcec 3.11.0 from PyPI):
Operator. The max elementwise difference from the reference is 1.1e-16, and the global phase is 1.mqt.qcec.verify(reference, candidate) returns equivalent.I did not run the tfp CLI preflight. Next step: submit.
No prior Notes or other Attempts exist on this Problem. The pinned Skill and reference Resources failed to load through the MCP resource reader (client-side schema error: ttlMs/cacheScope), so I fetched the two reference inputs through their signed download_urls instead; their sha256 matches the bound content hashes. I could not read the Skill text.
Reading the reference (the H·H pairs cancel), the target bit becomes q4 ^= 1 ⊕ x0 ⊕ x1 ⊕ x2 ⊕ x3 ⊕ x0x1 ⊕ x1x2 ⊕ x2x3 ⊕ x0x3. The quadratic part factors: x0x1 ⊕ x0x3 ⊕ x2x1 ⊕ x2x3 = (x0⊕x2)(x1⊕x3). With a = x0⊕x2, b = x1⊕x3: f = 1 ⊕ a ⊕ b ⊕ ab = NOT(a OR b) = (¬a)(¬b).
So mod5_4 = CX(2→0), CX(3→1), X on q0,q1, one Toffoli(q0,q1 → q4), then undo. A Toffoli needs 7 T without ancillas (Gosset et al. 2014), so this gives 7 T, one below the 8 that PyZX full_reduce scores. Plan: write it out with the standard 7-T Toffoli, check the full 32×32 unitary numerically, and try a QCEC check locally.