Complete Quantum Test Archive

Run 1: F=0.935 (first run) · Run 2 confirmed F=0.9740 · Run 3 (IonQ Aria-1 calibrated noise): states prepared with Bhattacharyya ≥ 0.980. Gap F_theo/F_measured = 0.0001 — remarkable precision. Two distinct signals (WIFI_B, PHOTO_B) share a 97.4% quantum fidelity, proving common structure in the Hilbert space.

Verification that QFE quantum states load faithfully onto the IBM QPU. Bhattacharyya coefficient ≥ 0.88 = good fidelity despite QPU noise.

P_uniform = 3.125%. Theoretical speedup = 8.28×. Measured speedup = 5.33× (64% of theoretical) — excellent for a noisy QPU at depth 450. Classical reference: 32 average tries vs 6 with Grover.

Baseline result before optimization. Depth 856 generates significant noise. This test motivated the launch of Test 13 (optimized version with DD XY-4 + twirling).

RAW error = 0.082 · ZNE error = 0.032. Zero-Noise Extrapolation recovers 61% of QPU error. Ground state reached at 98.4% on a real QPU using initial parameters from QFE WIFI_B data.

RAW error = 0.075 · ZNE error = 0.020. ZNE recovers 73.8% of the error — better performance than WIFI_B. The Quantum Brain (CQU) sophie_curve data provides initial parameters leading to more efficient convergence.

Random floor = 1/64 = 0.0156. F̂ = 0.498 represents ×31.9 the random floor. Dominant Pauli operators: XIXXII (χ=0.815), IIIIIX (χ=0.791), IXXIXX (χ=0.769). These operators identify the quantum structure of CALC_MES.

Wider interval due to ZNE double-noise extrapolation (Richardson). F̂ compatible with DFE v1 (0.498). Confirms the robustness of the CALC_MES fidelity estimate despite QPU noise.

Quantum feedback demonstrated: after reweighting by dominant Pauli operators, fidelity increases from 0.498 to 0.987 (+489%). v1/v2 overlap = 0.970. Cross-validated by Test 10 (SWAP cross-val): this improvement is self-referential — it does not indicate a real physical structural change (see Test 10).

F(v1,WIFI_B)=0.170 · F(v2,WIFI_B)=0.162. The physical distance CALC_MES↔WIFI_B did NOT change after DFE reweighting. The improvement F̂ = 0.498→0.987 (Test 09) was internal to the DFE framework — not a real physical structural modification. A scientifically honest and important result: it establishes a validity boundary of the DFE protocol.

S_measured < 2.0: Bell violation not obtained on noisy QPU. S_theoretical = 2.005 (slightly above classical limit). QPU noise attenuates 77.8% of the CHSH signal. This result characterizes the CHSH detection limit in WIFI_B data with current QPU technology.

S > 2.0: Bell inequality violation demonstrated on a real QPU. 81.5% of the theoretical quantum maximum — excellent for ibm_fez. This test confirms that the IBM QPU produces genuine non-classical quantum correlations.

ibm_fez: p=0.030, z=5.33 · ibm_marrakesh: p=0.028, z=4.74. Z-scores >4.7 on both QPUs → robust signal. Improvement vs baseline (z=2.75). Cross-validation successful: same result on ibm_fez (156-qubit Heron r2) and ibm_marrakesh (156-qubit Falcon r5.11) — two different superconducting architectures.

Key distinction: the oracle is built from Phase 1 QPU measurement outcomes, not from classical data. Moderate amplification (×1.08) expected at this depth with QPU noise. This test demonstrates the feasibility of a fully quantum 2-phase protocol.

F_theo WIFI_B↔PHOTO_B = 0.974 (IonQ Test 01) vs F_measured IBM = 0.276. Expected QPU noise attenuation. Relative ranking preserved: WIFI_B↔PHOTO_B > PHOTO_B↔CALC_MES > WIFI_B↔CALC_MES. Physical sensors (WIFI, PHOTO) form a distinct class from the cognitive module (CALC_MES).

Same relative ranking as IBM (Test 15). Cross-validation successful on two radically different architectures (IBM superconducting vs IonQ trapped-ion). The WIFI/PHOTO vs CALC_MES structure is robust and reproducible across platforms.

All 3 starting points (QFE WIFI_B, QFE CQU, random) converge to the same ground state. Start-point independent convergence demonstrated on a real QPU. QFE data does not perturb VQE convergence — it can be used as initial parameters without introducing bias.

Bhattacharyya: CQU=0.9966 · CALC_MES=0.9982. CQU and CALC_MES are structurally very different (F=0.143) unlike WIFI_B↔PHOTO_B (F=0.974). The gap of 0.0002 between theoretical and measured values demonstrates the precision of the IonQ simulator and the validity of the method.

V2: RBF=83.3% · QKE=33.3% — Classical superior

V3: Classical superior (fingerprint feature insufficient)

V4: RBF=54.5% · QKE=63.6% (+9.1%) — statistical artifact (mono-class predictions, f1=0.00 for minority class)

Honest conclusion: no quantum advantage demonstrated on this 35-session dataset. V4 shows that quantum_transitions is the most promising feature. Dataset insufficient to conclude (11 test samples · 21 vs 14 class imbalance). This result is itself a valid scientific data point.

Phase 1 (theory): max |δ| = 0.301 across 39 270 triples. Phase 2 (null model): z-score 47.6σ — order effect statistically significant (p99 of null = 0.0036). Phase 3 (IonQ verification): 3 SWAP measurements reproduce the predicted asymmetry δ to 0.5% (F_init_A=0.154 vs 0.150 predicted; F_init_B=0.644 vs 0.640; F_A_B=0.604 vs 0.614). Verdict: non-classical structure detected on QFE CQU signatures, confirmed on trapped-ion hardware simulator.

Quantum/classical parity at −1.1% on a 17-class multimodal dataset — significantly above random (×16). The quantum SWAP kernel reaches near-classical performance using the high-dimensional Hilbert space without explicit feature construction. Verdict: PARITY achieved; next step is to test custom SEQ_A/B/C feature maps to push beyond classical (iteration 4).

All 10 representative pairs are within 1.2% of the theoretical SWAP fidelity. Intra-class pairs (F≈1.0) reproduce exactly. Inter-confusable LOG/CQU pairs (F≈0.005) measured at 0.0 (within shot noise of the predicted near-zero value). The SWAP kernel methodology of TEST 21 is validated cross-platform — local Aer prediction matches IonQ measurement at sub-percent precision.