Hardware Validation — SCPN-Quantum-Control

+17.48%DLA Parity Asymmetry

342Phase 1 Circuits

21Reps per Point

p = 0.035Binomial Significance

Phase 1 — DLA Parity Asymmetry Confirmation (April 2026)

First publishable hardware result

The dynamical Lie algebra of the XY Hamiltonian splits as su(even) ⊕ su(odd) under the parity operator P = ∏_i Z_i. The SCPN framework predicts that the two sectors respond differently to hardware decoherence, with the odd (“feedback”) block being more robust than the even (“projection”) block. This has now been confirmed empirically on ibm_kingston (Heron r2, 156 qubits).

Protocol: equal-depth Trotter circuits prepared in known parity eigenstates, measured in the computational basis, with parity leakage defined as the fraction of shots that end in the opposite parity sector. Parity is exactly conserved by the ideal XY evolution, so any leakage is a direct measure of decoherence.

Trotter Depth	ISA Gate Count	Leakage (even)	Leakage (odd)	Relative Asymmetry	Reps
2	50	8.06%	8.27%	−2.5% (baseline noise)	12
4	88	9.82%	8.62%	+13.98%	21
6	126	12.91%	10.99%	+17.48%	21
8	164	14.43%	12.84%	+12.41%	21
10	202	16.58%	14.95%	+10.91%	21
14	278	18.98%	17.97%	+5.58%	21
20	392	22.95%	21.14%	+8.55%	12
30	582	27.71%	25.76%	+7.58%	12

Statistical Significance

Seven of eight depth points show positive asymmetry (even sector leaks more than odd sector). Binomial test under the null hypothesis p = 0.5 gives p = 0.035, significant at the standard 5% level.

Magnitude vs Prediction

Mean relative asymmetry across depths ≥ 4: +10.8%. The apriori classical simulator range was 4.5–9.6%, so the observed signal sits at the upper end of the prediction window.

Clean Decoherence Profile

Parity leakage grows smoothly from ~8% at depth 2 to ~28% at depth 30, providing a directly usable noise profile for calibrating the GUESS symmetry-guided error mitigation scheme in Phase 2.

Independent n = 8 Probe

Two scaling probes at n = 8, depths 4 and 8, reproduced the same directional asymmetry (+3.0% and +1.7% respectively). Phase 2 will extend this to higher n and apply GUESS mitigation for bias correction.

IBM Heron r2 Hardware Specifications

Platforms

ibm_kingston (Phase 1, April 2026) and ibm_fez (legacy, February 2026): 156 fixed-frequency transmon qubits each. Tunable couplers. Median CZ gate error: ~0.3–0.5%. T1 ≈ 300 µs. T2 ≈ 200 µs. Heavy-hex connectivity. Accessed via Qiskit Runtime with V2 Estimator and Sampler primitives.

Legacy Experiments (ibm_fez, February 2026)

Experiment	Qubits	CZ Depth	Hardware Result	Exact Value	Relative Error
VQE ground state energy	4	12	−6.2998	−6.3030	0.05%
Kuramoto XY dynamics (1 Trotter rep)	4	85	R = 0.743	R = 0.802	7.3%
Kuramoto XY dynamics (3 Trotter reps)	4	255	R = 0.581	R = 0.802	27.6%
Qubit scaling test	6	147	R = 0.482	R = 0.532	9.3%
UPDE-16 snapshot	16	770	R = 0.332	R = 0.615	46%
Bell inequality (CHSH)	2	3	S = 2.165	S = 2√2	>8σ violation
BB84 QKD protocol	1	2	QBER = 5.5%	<11% threshold	Secure
State preparation fidelity	4	8	F = 0.946	F = 1.0	5.4%

Key Findings

Coherence Wall at Depth 250–400

Clear transition from quantum-dominated to noise-dominated regime. Single Trotter rep (depth 85) maintains 7.3% error; 3 reps (depth 255) degrades to 27.6%. UPDE-16 at depth 770 is fully noise-limited.

Error Mitigation Effectiveness

ZNE with Richardson extrapolation reduces VQE error from 2.1% to 0.05%. Z₂ parity post-selection discards ~15% of shots but improves fidelity by ~8%. Dynamical decoupling extends useful depth by ~20%.

Quantum Entanglement Certified

CHSH S = 2.165 exceeds classical limit 2.0 by >8 standard deviations. Proves genuine quantum correlations in synchronised oscillator states — not simulable classically.

QKD Below Security Threshold

BB84 quantum bit error rate of 5.5% is well below the 11% security threshold. Demonstrates that synchronisation-based quantum states can support cryptographic protocols.

Decoherence Analysis

Error Sources

Gate errors: Median CZ fidelity ~99.7%. Accumulates as 0.3% × N_CZ.
Readout errors: ~1% per qubit. Mitigated by readout error correction matrix.
Crosstalk: Heavy-hex topology minimises but does not eliminate simultaneous-gate crosstalk.
T1 relaxation: Circuit execution time < T1 for shallow circuits. Dominates at depth >400.
T2 dephasing: Phase coherence decays exponentially. Primary limit for phase-sensitive Kuramoto measurements.

Multi-Platform Support

IBM Quantum Production

Full support via qiskit-ibm-runtime. V2 Estimator + Sampler. Automatic transpilation. Error mitigation pipeline. Tested on Heron r2 (156q) and Eagle (127q).

Trapped-Ion Stable

Noise models for trapped-ion hardware. All-to-all connectivity. Higher gate fidelity, lower gate speed. Heating and motional dephasing models.

GPU Simulation Stable

CuPy + JAX backends for GPU-accelerated state vector simulation. Up to 30 qubits on A100. Useful for circuit development before hardware submission.

Circuit Cutting Experimental

Decomposes large circuits into subcircuits executable on smaller devices. Wire cutting and gate cutting. Polynomial overhead in post-processing.