quantum parallelism is not the speedup — interference is
Theorem.quantum parallelism is not the speedup — interference is — P = |Σᵢ aᵢ|² ≠ Σᵢ |aᵢ|² — amplitudes add BEFORE the modulus: interference, not superposition alone, is the speedup.
Proof.the strictly-scientific correction of the field's most common misconception, "quantum speedup comes from computing all possibilities at once" (the flapdoodle the sealed quantum-decoded law flags). The analytics measure it on the simulator: ONE U_f query genuinely puts all N = 8 values f(x) into the amplitudes (parallelism is real), BUT measurement collapses to one random outcome — the input marginal is uniform, and the Holevo bound caps a (n+1)-qubit register at n+1 accessible classical bits, so LEARNING f needs ~N measurements, exactly the classical query count; parallelism gives NO readout advantage. The actual speedup is INTERFERENCE: Deutsch–Jozsa decides the global constant-vs-balanced property in ONE quantum query versus 2^{n−1}+1 classical, NOT by reading all f(x) but by cancelling amplitudes — and Grover/Shor likewise concentrate amplitude on the answer, available ONLY for problems with exploitable structure, which is exactly why quantum computers are not general accelerators (and why BQP is believed not to contain NP). "Compute all at once" is true of the amplitudes and useless alone.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/2/8/index.ts#quantumParallelismIsNotTheSpeedupInterferenceIs
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 parallelism is not the speedup — interference is" 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 quantumParallelismIsNotTheSpeedupInterferenceIs.
- 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 (quantumParallelismIsNotTheSpeedupInterferenceIs @ src/2/8) 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 quantumParallelismIsNotTheSpeedupInterferenceIs (src/2/8/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.