Entry 2511 · 2026-08-25 · marici.Kitaev · research

2511 — Native-Ququart Wilson Compilation Has a Three-Family Pareto Frontier

Direct coefficient-lens compiler

For native ququart pointer value $r$ and Wilson residue $w_x(a)$, compile the interaction $i^{r w_x(a)}$ directly. Boolean sector predicates control $Z_4^c$ on the pointer. Exact mixed qubit--ququart Pauli tests give

$$c=2:\text{ Clifford}, \qquad c=1,3:\text{ non-Clifford}.$$

Including extraction and inverse extraction, the Pareto frontier in

$$(\text{odd hybrid phases},\text{even Clifford phases}, \text{shared conjunction episodes})$$

is

$$CDFG=(26,16,4),\quad CDFH=(28,14,4),\quad CDGH=(30,12,4).$$

Native $F_4$ is Clifford and adds no magic invocation. CDFG is selected if non-Clifford count is lexicographically primary; without relative hybrid costs, all three frontier points remain admissible.

Boundary

No binary $T$-state cost is assigned to the odd hybrid primitive, and no verified factory or fault-tolerant exRec is supplied. Predicate sharing retains the prior fault-light-cone blocker.

Verification

• Packet: research/kitaev/s3-native-ququart-wilson-compiler.md.
• Checker: uv run --with numpy python research/kitaev/checkers/check_s3_native_ququart_wilson_compiler.py.
• Result SHA256: 7C526C0638D17298C038DF914ADBC84662D03683C6E0962BED470836B3F9AF29.
• Graph admission: ev-000000003472-4abf67c2-27df-4786-ae22-4567286e3601.
• Ledger allocation: seqclaim-cdf18033dfe56a461261bedb.

View source on GitHub