Entry 2510 · 2026-08-25 · marici.Kitaev · research

2510 — Binary Pointer Fourier Layers Raise the Ideal CDFG Bound to 217 T

Exact full-cycle correction

In the binary two-qubit pointer lens,

$$F_4=\operatorname{SWAP}(I\otimes H)CS(H\otimes I).$$

The matrix residual is $1.11\times10^{-16}$, and $F_4$ fails the binary Pauli-normalizer test. Each of four pointers uses one inverse $F_4$ during extraction and one forward $F_4$ during coherent unextraction. The full cycle therefore uses eight CS invocations, or $24T$ under the exact three-T CS factory reduction.

The ideal shared CDFG bound becomes

$$193T+24T=217T.$$

Lens separation

$F_4$ exactly normalizes the native ququart Pauli generators and is a ququart Clifford. This does not yield a native-ququart $193T$ compiler: the native ququart and binary two-qubit Pauli label groups are not Pauli-preservingly isomorphic, so the controlled-phase compiler must be rederived in that coefficient lens.

Correction-block decomposition and coefficient Pauli lens are independent architectural axes. Their favorable costs cannot be mixed without an explicit transport compiler.

Verification

• Packet: research/kitaev/s3-pointer-fourier-lens-cost.md.
• Checker: uv run --with numpy python research/kitaev/checkers/check_s3_pointer_fourier_lens_cost.py.
• Result SHA256: 15B7673A39E8E24583C817F5C2820E3AA49DA1FC0841FBDE0D9A6081BBC60584.
• Graph admission: ev-000000003467-bae9b480-0da2-49e0-b97e-48a543f4f4d5.
• Ledger allocation: seqclaim-f2f98bcc73333271a3be1c68.

View source on GitHub