Benchmarks — SCPN-Quantum-Control

Rust Engine Performance

PyO3 Rust extension with Rayon parallelisation. Benchmarked against pure Qiskit on identical workloads.

Operation	Qiskit (Python)	Rust Engine	Speedup
Hamiltonian construction (declared warmed baseline, L=4)	See committed native-speed benchmark		96.5×
ICI three-level evolution (2,000 pts)	68.30 ms	0.04 ms	1,665×
Pauli string operations	95 ms	0.12 ms	792×
K_nm matrix utilities	180 ms	0.4 ms	450×
DLA dimension computation	340 ms	1.2 ms	283×
OTOC evaluation	520 ms	2.1 ms	248×
Krylov complexity	410 ms	1.8 ms	228×
Lindblad operators	290 ms	1.5 ms	193×
Kuramoto order parameter	45 ms	0.3 ms	150×
(α,β)-hypergeometric envelope (₂F₁)	scipy loop	custom series	44×

134 Rust functions exported via PyO3 across 37 source files. ndarray + num-complex + rayon. Edition 2021. Rust vs Python parity verified at 4.97×10⁻¹⁴ for the ICI integrator.

Hardware Validation Summary

Experiment	Qubits	Depth	Hardware	Exact	Error
VQE ground state	4	12 CZ	−6.2998	−6.3030	0.05%
Kuramoto XY (1 rep)	4	85	R=0.743	R=0.802	7.3%
Qubit scaling	6	147	R=0.482	R=0.532	9.3%
UPDE-16 snapshot	16	770	R=0.332	R=0.615	46%

IBM ibm_fez (Heron r2, 156 qubits). February 2026. 33 jobs, 176,000+ shots.

Phase 1 Campaign — DLA Parity Asymmetry (ibm_kingston, April 2026)

Depth	Reps	Even sector leakage	Odd sector leakage	Asymmetry	Welch p
2	12	8.06%	8.27%	−2.5%	0.446
4	21	9.82%	8.62%	+13.98%	1.45×10⁻⁶
6	21	12.91%	10.99%	+17.48%	6.61×10⁻⁶
8	21	14.43%	12.84%	+12.41%	8.89×10⁻⁵
10	21	16.58%	14.95%	+10.91%	6.67×10⁻⁶
14	21	18.98%	17.97%	+5.58%	0.00995
20	12	22.95%	21.14%	+8.55%	0.00666
30	12	27.71%	25.76%	+7.58%	0.00955

342 circuits, 4 qubits, 8 Trotter depth points. Fisher's combined χ² = 123.40 (df = 16), combined p ≪ 10⁻¹⁶. Follow-up popcount controls found substantial same-popcount within-sector variation; the promoted wording is parity-sector and excitation-number correlated leakage asymmetry, not DLA parity alone.

Quantum Certification

Bell Inequality (CHSH)

S = 2.165 ± 0.022 for q0–q1 (7.54σ) and S = 2.188 ± 0.021 for q2–q3 (8.94σ), recomputed from committed counts.

Matched-basis mismatch re-run

Fresh raw rates span 1.39%–3.00% and mitigated rates 0.51%–1.33%. The legacy 5.5% value is not derivable from its artefact; no QKD security, key-rate, or viability claim follows.

State Fidelity

94.6% preparation fidelity. 20/20 experiments successful. Coherence wall identified at depth 250–400.

Coherence Limitations

Depth 250–400: The Heron r2 Coherence Wall

Beyond ~250 CZ gates, decoherence dominates. The 16-qubit UPDE experiment (depth 770) shows 46% error — consistent with known T1/T2 limits. Error mitigation (ZNE, PEC, DD) reduces but does not eliminate this. Future fault-tolerant hardware will lift this ceiling.

Classical vs Quantum Scaling

Crossover Estimation

At the system sizes reached here (up to 16 qubits), classical ODE, exact, and tensor-network solvers are faster and more accurate. No broad quantum advantage is claimed; the value is controlled characterisation and auditable hardware evidence.

MPS Baseline

Committed MPS baselines reproduce the 16-qubit UPDE observable to 6.3×10⁻⁴ at bond dimension 2 and converge for Kuramoto-8 at bond dimension 4. These classical baselines bound, rather than advertise, the hardware route.