# ADRIZ-Q real-QPU rigor analysis

**Job** `d911mveu9n7c73alroig` on **ibm_kingston** (53 quantum-seconds, 87 circuits, one SamplerV2 batch). Offline post-processing of the full per-circuit hardware counts. No IBM key read.

## Optimisation / QUBO cards — measured optimum probability vs the random null

| card | n_qubits | optimum | p_opt (HW) | random-null p_opt | concentration xnull | approx-ratio [95% CI] | TVD(hw,sim) | honest verdict |
|---|---|---|---|---|---|---|---|---|
| OPT1_mogi_single | 8 | 495.5 | 0.0061 | 0.0039 | 1.6 | 0.023 [0.019, 0.027] | 0.202 | CONCENTRATED |
| OPT2_multisource_p1 | 8 | 154.8 | 0.0010 | 0.0039 | 0.2 | 0.770 [0.763, 0.776] | 0.201 | BEST-OF-N only |
| OPT3_assoc_maxcut_p4 | 10 | 27.6 | 0.0295 | 0.0059 | 5.0 | 0.829 [0.825, 0.833] | 0.565 | CONCENTRATED |
| OPT4_siteselect_p3 | 8 | -4.22 | 0.0073 | 0.0078 | 0.9 | 0.332 [0.323, 0.340] | 0.170 | BEST-OF-N only |
| OPT5_insar_unwrap | 8 | 1 | 0.0105 | 0.0078 | 1.3 | 0.911 [0.908, 0.914] | 0.279 | BEST-OF-N only |
| OPT6_dozier_subpixel | 8 | 0.02535 | 0.0195 | 0.0039 | 5.0 | 0.191 [0.180, 0.202] | 0.163 | CONCENTRATED |
| OPT7_plume_so2 | 8 | 0.1172 | 0.0015 | 0.0039 | 0.4 | 0.787 [0.781, 0.793] | 0.204 | BEST-OF-N only |
| OPT8_spectral_unmix | 6 | 28.87 | 0.0642 | 0.0156 | 4.1 | 0.152 [0.142, 0.162] | 0.145 | CONCENTRATED |
| OPT9_fusion_tasking_p4 | 8 | -0.83 | 0.0110 | 0.0039 | 2.8 | 0.596 [0.591, 0.602] | 0.156 | CONCENTRATED |
| N1 | 6 | 154.8 | 0.0117 | 0.0156 | 0.8 | 0.713 [0.706, 0.721] | 0.194 | BEST-OF-N only |
| N2 | 9 | 3.499 | 0.0657 | 0.0039 | 16.8 | 0.649 [0.643, 0.654] | 0.217 | CONCENTRATED |
| N3 | 10 | 21.82 | 0.0400 | 0.0020 | 20.5 | 0.593 [0.588, 0.598] | 0.346 | CONCENTRATED |

## MLAE / QAE cards — did the quantum quadratic edge survive hardware?

| card | p_true | n_queries | HW abs-err | sim abs-err | MC mean abs-err [95% CI] | HW below MC CI-lo? | verdict |
|---|---|---|---|---|---|---|---|
| N4 | 0.250 | 8960 | 0.0023 | 0.0007 | 0.0042 [0.0034, 0.0051] | YES | edge survived |
| N6 | 0.500 | 8576 | 0.0022 | 0.0006 | 0.0043 [0.0034, 0.0052] | YES | edge survived |
| N7 | 0.193 | 8960 | 0.0032 | 0.0005 | 0.0031 (no CI; sim-only prototype) | n/a | edge eroded (HW err > MC mean) |

## Kernel cards — classification stays classical-favoured under shot noise

Full-data AUC is the defensible classification verdict; the n=6 landmark LOO-AUC is statistically degenerate (flagged) and the hardware metric of record is the fidelity-entry shot-noise RMSE.

| card | n_qubits | exact-sim QK AUC (full) | matched RBF AUC (full) | HW kernel-entry RMSE vs sim | landmark AUC (degenerate n=6) | verdict |
|---|---|---|---|---|---|---|
| N5 | 4 | 0.836 | 0.952 | 0.013 | 0.000 (degenerate) | CLASSICAL-favoured / TIE |
| N8 | 4 | 0.782 | 0.935 | 0.051 | 0.000 (degenerate) | CLASSICAL-favoured / TIE |
| N9 | 4 | 0.969 | 0.999 | 0.022 | 0.000 (degenerate) | CLASSICAL-favoured / TIE |
| N10 | 4 | 0.910 | 1.000 | 0.025 | 0.444 (degenerate) | CLASSICAL-favoured / TIE |

## Overall honest finding

Of the 12 optimisation/QUBO cards run on real hardware, **7 genuinely CONCENTRATED** probability on the optimum above the uniform-random null (OPT1_mogi_single, OPT3_assoc_maxcut_p4, OPT6_dozier_subpixel, OPT8_spectral_unmix, OPT9_fusion_tasking_p4, N2, N3), while **5 were BEST-OF-N only** (OPT2_multisource_p1, OPT4_siteselect_p3, OPT5_insar_unwrap, OPT7_plume_so2, N1) — the optimum surfaces because 4096 shots over <=10 qubits will catch it, not because the QPU put weight there — and **0 did not surface the optimum at all** (none). This replaces the blanket 'every optimisation card recovered the optimum' claim with the honest distribution-level picture: best-of-N recovery is real but weak; only the cards whose measured p_opt exceeds the null by >1.5x are a true quantum-concentration signal.

On the **sensing/estimation** lane, the quantum quadratic edge SURVIVED hardware on N4, N6 (HW MLAE abs-err below the classical-MC 95% CI lower bound at matched query budget). The amplitude-estimation lane remains the place quantum genuinely helps.

On the **classification (kernel)** lane, every card stays classical-favoured or a TIE: the matched classical RBF AUC meets or beats the quantum-kernel AUC on full data, and shot noise degrades the small landmark kernel further on hardware. No quantum advantage in classification (the dimensionality wall holds) — confirmed on hardware, not asserted.