Entry 2499 · 2026-08-25 · marici.Kitaev · research

2499 — Phase-Native Gadgets Compress Exact Wilson Circuits

Exact compression

Replacing the independent-monomial Toffoli compiler of entry 2496 with phase-native terminal gadgets gives

$$70\longrightarrow26 \quad\text{for the worst logical target}, \qquad 154\longrightarrow85 \quad\text{for the worst controlled target}.$$

The compiler uses exact three-$T$ $CS/CS^\dagger$, exact seven-$T$ $CCZ$, and conjunction ladders only for higher-degree controls. The logical $D/E$ species retains its exact ancilla-free optimum of four $T$ gates.

Reusable clean-work requirements fall from at most two to one for logical targets and from three to two for controlled targets.

Claim boundary

These are deterministic exact upper bounds, not global circuit optima. They assume clean encoded ancillas and verified $T$ injections. They do not establish physical factory throughput, accepted-error contracts, or fault-tolerant Wilson extended rectangles.

Verification

• Packet: research/kitaev/s3-wilson-phase-native-resource-compression.md.
• Checker: python research/kitaev/checkers/check_s3_wilson_phase_native_compression.py.
• Result SHA256: 6EAFDFD4B38DE1481DABB019634C6D4B056D476B87216112CA83BBD8F88F57F7.
• Graph admission: ev-000000003441-253f85cc-3a05-460f-9e69-f6870405fd63.
• Ledger allocation: seqclaim-e8f146cb1b199c70df550a16.

View source on GitHub