the variational quantum eigensolver and QAOA — working hybrid solvers
Theorem.the variational quantum eigensolver and QAOA — working hybrid solvers — E(θ) = ⟨ψ(θ)|H|ψ(θ)⟩ ≥ E₀ — classical minimisation over quantum evaluations.
Proof.the hybrid frontier developed to real solvers over the sealed src/0 gate set: VQE minimises ⟨ψ(θ)|aZ+bX|ψ(θ)⟩ over the RY(θ) ansatz and returns the exact ground energy −√(a²+b²) for four Hamiltonians, matching exact diagonalisation — the variational principle on a real state-vector circuit; QAOA's p=1 circuit e^{−iβΣX}·e^{−iγC}|+⟩³ on the triangle MaxCut reaches ⟨C⟩ = 1.999 at the optimised angles, above the random-cut baseline 1.5 and essentially at the true max cut 2. Both are quantum-circuit expectations optimised by a classical outer loop (the real VQE/QAOA structure); deterministic simulations — the algorithm's shape, not physical speedup; the grid optimiser stands in for gradient descent, barren plateaus named not solved.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/2/8/index.ts#variationalQuantumEigensolverAndQaoa
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
"the variational quantum eigensolver and QAOA — working hybrid solvers" 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 variationalQuantumEigensolverAndQaoa.
- 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 (variationalQuantumEigensolverAndQaoa @ 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 variationalQuantumEigensolverAndQaoa (src/2/8/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.