quantum-computing logic reviewed for shared usability — one MCX ladder, classical = quantum on the basis
Theorem.quantum-computing logic reviewed for shared usability — one MCX ladder, classical = quantum on the basis.
Proof.the shared-usability audit of all quantum-computing logic in src, sealed: (1) the state-vector layer is already DRY — src/9/1's operator algebra (gateMul, commutator, anticommutator, pauliAlgebraCloses) and its ~15 algorithms (deutschJozsa, simon, bb84, teleportQubit, ghzMermin, bernsteinVazirani, superdense, …) all import ONE gate table (GATES, flat-8 complex) and ONE QuantumState from src/0, reusing applyGate/cnot/measure/qubits — NO quantum primitive defined twice; (2) the classical reversible gates rnot·rtoffoli (src/1/9) and rcnot (src/4/6) are one k-controlled-flip ladder — all three equal mcFlip(bits, target, controls) at 0/1/2 controls, verified over every 3-bit pattern — currently funnelling through no shared primitive (the one fragmentation); (3) the classical reversible gate IS the quantum gate on the basis — src/0's unitary cnot|b⟩ and toffoli|b⟩ permute the index exactly as rcnot(b) and rtoffoli(b): two representations, one object. mcFlip is the canonical shared primitive, the correspondence the bridge; minor barrel gap noted (mind re-exports cnot but not toffoli).
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/fire/physics/index.ts#reversibleGatesFunnelThroughOneMcxAndAreTheQuantumBasisPermutation
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"quantum-computing logic reviewed for shared usability — one MCX ladder, classical = quantum on the basis" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation reversibleGatesFunnelThroughOneMcxAndAreTheQuantumBasisPermutation.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (reversibleGatesFunnelThroughOneMcxAndAreTheQuantumBasisPermutation @ src/fire/physics) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes reversibleGatesFunnelThroughOneMcxAndAreTheQuantumBasisPermutation (src/fire/physics/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.