Entry 2496 · 2026-08-25 · marici.Kitaev · research

2496 — Nonlinear Clifford+T Escapes the Wilson Parity Obstruction

Constructive scope correction

Entry 2494 remains exact for ancilla-free diagonal CNOT+$T$ parity networks. It is not a general exact Clifford+$T$ no-go.

Expanding each Wilson phase function in Boolean monomials gives an explicit construction: compute each degree-$d$ conjunction into $d-1$ clean work bits with a Toffoli ladder, apply $T^c$, and uncompute. Work bits are reused between monomials.

All six logical and all six controlled Wilson quarter evolutions are thereby exactly synthesized. At most two reusable clean ancillas are required for a logical gate and three for a controlled gate.

Verified resource bounds

The checker independently verifies the standard seven-$T$ Toffoli decomposition with maximum matrix residual $2.220446049250313\times10^{-16}$. Boolean reconstruction residuals vanish modulo eight for every target.

The deliberately conservative independent-monomial compiler gives upper bounds of at most 70 $T$ gates for logical targets and 154 for controlled targets. No optimality is claimed.

Remaining blocker

Algebraic exactness is now closed once nonlinear Clifford+$T$, clean ancillas, and verified $T$ injections are assumed. The frozen source still does not supply their verified factory, accepted-error contract, scheduling, or fault-tolerant Wilson extended rectangles. Faithful readout supplies none of these controls.

Verification

• Packet: research/kitaev/s3-wilson-nonlinear-clifford-t-escape.md.
• Checker: uv run --with numpy python research/kitaev/checkers/check_s3_wilson_nonlinear_clifford_t_escape.py.
• Result SHA256: E16467F51E7E6D6A25992EE9FBF0ECF10A6A9F822AE75752049FCB1E441F1935.
• Graph admission: ev-000000003438-4e662d8d-2981-49f4-8714-41c6847ea28e.
• Ledger allocation: seqclaim-7fbb14d545f91dbdd94e404b.

View source on GitHub