Research protocol for the six-level breakthrough ladder. Protocols live in experiments/level-N-<slug>/protocol.md. Artifacts go to experiments/results/YYYY-MM-DD/level-N/. See RESEARCH.md for the master doc.

Level 1 — Statevector

Hypothesis: full-featured statevector sim in a browser tab, reaching bandwidth-bound performance. Pass bar: F ≥ 1 − 1e-5 vs CPU reference, ≥ 40% of peak memory BW at N ≥ 22, T(N) slope ≈ 1.0 at N ≥ 18.

Level 2 — MPS

Hypothesis: a CPU-only MPS / DMRG simulator in a browser tab reaches ≥ 72 qubits for low-entanglement circuits, with χ-bounded error that tracks bipartite entropy, and DMRG ground-state energies converge to the analytical thermodynamic limits for the textbook 1D models. Pass bars: (E5) F ≥ 0.999 vs CPU statevector at χ = 64 on every cell; (E6) no OOM and median sweep ≤ 1 s at N = 72, χ = 32, depth = 4; (E7) fit slope of log₂(χ_req) vs depth within 1.0 ± 0.2; (E18, Phase B) DMRG TFIM E/N converges toward Pfeuty's −4/π; (E19, Phase B) DMRG Heisenberg AFM E/N converges toward Bethe's J·(1/4 − ln 2).

Level 3 — Kernel fusion

Hypothesis: fusing k single-qubit gates on the same qubit into one dispatch collapses α — the fixed dispatch cost from E4 — by a factor of k. Pass bars: (E8) fused = unfused at F ≥ 1−1e-5 on all cells; (E9) α_eff(32) ≤ α_eff(1)/16 AND ≤ 20 μs; (E10) best speedup ≥ 2× AND N=20 regression-free (≥ 1.05×). Scope note: only same-qubit chains are fused; layer fusion across different qubits (brick-wall) is deferred to a future kernel.

Level 6 — Chemistry

Hypothesis: (E16) VQE on H₂ in STO-3G with a hardware-efficient ansatz reaches chemical accuracy (|ΔE| ≤ 1.6 mHa) at every bond length; (E20, Phase C v1) VQE on LiH in STO-3G s-only (6 qubits) with HEA L=6 + L-BFGS reaches chemical accuracy at the equilibrium bond length; (E21, Phase C v2) VQE on BeH₂ in STO-3G s-only (8 qubits, 256-dim) with HEA L=10 + L-BFGS reaches chemical accuracy on the best-of-5 trials at R = 1.34 Å. All three Hamiltonians built from molecular integrals on the fly; reference E_FCI is the Jacobi-diagonalized spectrum projected to the physical particle-number sector.

Levels 4–5 — deferred