quantum adds no computability (Church–Turing–Deutsch)
Theorem.quantum adds no computability (Church–Turing–Deutsch) — CNOT·(H⊗I)|00⟩ = (|00⟩+|11⟩)/√2 computed exactly on a classical machine — the quantum circuit computes the same function class, no super-Turing power.
Proof.a Bell circuit (H, CNOT) evolves to (|00⟩+|11⟩)/√2 by exact state-vector arithmetic on a classical CPU — every quantum circuit is classically simulable, so BQP ⊆ decidable and the halting problem stays undecidable for quantum too (Deutsch 1985).
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveTwentySeven
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 adds no computability (Church–Turing–Deutsch)" 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 discoveredTheoremsWaveTwentySeven.
- 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 (discoveredTheoremsWaveTwentySeven @ src/9/1) 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 discoveredTheoremsWaveTwentySeven (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.