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 (8q)	2,701 ms	0.5 ms	5,401×
K_nm matrix utilities	180 ms	0.4 ms	450×
Pauli string operations	95 ms	0.12 ms	792×
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×

22 Rust functions exported via PyO3. ndarray + num-complex + rayon. Edition 2021.

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.

Quantum Certification

Bell Inequality (CHSH)

S = 2.165 — classical limit is 2.0. Violation by >8σ. Certifies genuine quantum entanglement in synchronised oscillator states.

QKD Bit Error Rate

QBER = 5.5% — below the BB84 security threshold of 11%. Quantum-secure key distribution validated on real hardware.

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

Classical Kuramoto simulation scales as O(N²) per timestep. Quantum XY evolution on ideal hardware scales as O(N) circuit depth with O(log N) measurement overhead. The quantum advantage crossover is estimated at N ≈ 200–500 oscillators on fault-tolerant hardware with logical error rates < 10⁻⁶.

MPS Baseline

Matrix Product State simulation provides efficient classical baseline for low-entanglement regimes. Included in benchmarks subpackage for honest comparison. MPS wins for weakly-coupled systems; quantum hardware wins for strongly-entangled synchronisation.