Quantum predictive advantage under shift usually requires known target labels. We derive the assumption-free sharp identified interval for the finite-batch advantage of a fixed candidate over the best member of a prespecified fixed classical-kernel family under any bounded loss and unrestricted completions of the unaudited labels; zero-one accuracy has exact closed-form partial-label updates. Across eight security shifts, zero-label upper endpoints against 115 classical kernels span 0.002-0.088. Retrospective auditing reduces every endpoint to 0.010 with 0-33 of 500 labels, including entangling-ZZ models. Prospective corroboration on two eligible tasks met predefined criteria: four task-classifier medians require 0-3 labels (overall median 0; maximum 76), and all 20 realized effects are negative; a third task fails its feature gate. Protocol controls reverse an apparent advantage, while finite-shot noise can increase predictive distinctness without useful advantage. The framework separates protocol validity, target predictive indispensability, and quantum relevance.
Comments
42 pages, 7 figures; 16-page Supplementary Information available as ancillary material. Submitted to EPJ Quantum Technology
Quantum predictive advantage under shift usually requires known target labels. We derive the assumption-free sharp identified interval for the finite-batch advantage of a fixed candidate over the best member of a prespecified fixed classical-kernel family under any bounded loss and unrestricted completions of the unaudited labels; zero-one accuracy has exact closed-form partial-label updates. Across eight security shifts, zero-label upper endpoints against 115 classical kernels span 0.002-0.088. Retrospective auditing reduces every endpoint to 0.010 with 0-33 of 500 labels, including entangling-ZZ models. Prospective corroboration on two eligible tasks met predefined criteria: four task-classifier medians require 0-3 labels (overall median 0; maximum 76), and all 20 realized effects are negative; a third task fails its feature gate. Protocol controls reverse an apparent advantage, while finite-shot noise can increase predictive distinctness without useful advantage. The framework separates protocol validity, target predictive indispensability, and quantum relevance.
Quantum Fourier sampling may help audit the spectral learnability of delay-based physical unclonable functions (PUFs). We ask whether that promise survives access matching, a strong classical comparator, and oracle synthesis. Three gates structure the evaluation. Structure: low degree is not small support at reachable challenge lengths; for 4-XOR at n=14, degree ≤df(0.1) admits 91% of all 2n characters and the median 90%-mass set spans a third of the spectrum. Algorithmics: constructing the phase oracle logically implies classical membership access, making Kushilevitz--Mansour the correct baseline; across 45 tasks it exhausts each finite domain, and no 4-XOR ideal-sampling case reaches 90% mass within 2n calls. A quantum-kernel diagnostic appears more favorable, with geometric difference rising to 2.151 at N=512 challenges, but it correlates 0.991 with 1/λmin(KC) for the classical Gram matrix KC, and the 4-XOR label-complexity ratio does not exceed a balance-preserving permutation null (p=0.930). Trace-normalized geometric difference can therefore grow through classical ill-conditioning alone, without task-label alignment. Implementation: a simulator-validated fixed-point phase oracle based on the quantum Fourier transform admits an 18.9% routed-depth reduction, yet the least certified precisions have estimated durations of 1.18--1.55× the median dephasing time T2 of the mapped qubits on a static backend snapshot, without hardware execution. We find no end-to-end advantage in the evaluated regime, although ideal sampling does use fewer coherent calls on the thresholded task. The contribution is the Three-Gate Quantum Audit Protocol: a reproducible procedure separating an ideal query advantage from a realizable security benefit. This is not a claim about deployed silicon and not an impossibility result.
A growing body of work has questioned whether quantum machine learning (QML) offers any genuine advantage over classical methods on realistic data, with recent results showing that many apparent quantum kernel advantages are reproducible by classical surrogates once sample size, hyperparameters, and estimator variance are properly controlled. We conduct a pre-registered, falsification-first investigation into one specific, previously unexamined variant of this question: does the causal sparsity of a data-generating process as opposed to generic statistical structure modulate quantum kernel advantage or variational quantum circuit (VQC) trainability? Using a controllable structural-causal-model (SCM) data generator, a moment-matched dense-null control, and a battery of eight experiments spanning tabular regression, PDE solving, and gradient-landscape diagnostics, we find: (i) an apparent quantum-kernel advantage at small sample sizes N>=200 that consistently vanishes and reverses sign by N(approx):300, uniformly across all tested sparsity levels; (ii) no causal link between data sparsity and this advantage, once tested against a properly matched non-causal control (factorial ANOVA interaction p=0.194); (iii) no genuinely-quantum causal contribution to predictive performance distinguishable from estimator noise at any tested condition, including the resolution of one apparent positive result as a single-seed statistical artifact; (iv) a dissociation between classical-shadow kernel-matrix reconstruction (which fails) and task-level dequantization (which succeeds), indicating that matrix fidelity is an unreliable proxy for classical simulability; (v) a previously undocumented, reproducible failure mode in the PHASE domain-decomposition PINN architecture's boundary-continuity constraint, whose removal yields a solver that is simultaneously faster and more accurate across the full tested regime; and (vi) a robust, reproducible, but ultimately unexplained resonance phenomenon in VQC gradient variance at specific integer causal-edge counts, for which we construct, pre-register, and subsequently falsify a candidate mechanistic explanation via out-of-sample prediction. We argue that the recurring pattern of apparent effects collapsing under targeted multi-seed and out-of-sample scrutiny is itself a methodologically important finding, and we recommend such validation be treated as a mandatory component of QML advantage claims rather than an optional check applied only to surprising results.
Claims of quantum advantage should remain robust even when classical strategies have access to side information correlated with the benchmark under evaluation, just as Bell certification must account for measurement dependence. We formalize such correlations as benchmark dependence, a task-level generalization of measurement dependence. For every bounded-reward task, we show that the optimal benchmark-dependent classical score obeys Sη≤min{1,Scl+η}, and construct a family of tasks that saturates this bound, showing that the linear dependence on η is tight without further assumptions. For repeated product tasks with roundwise dependence, we obtain the stronger multiplicative bound Sη(n)≤(ωc+η)n, and extend the framework to finite-sample data, mutual-information constraints, multipartite tasks, and correlations distributed along a causal path. Applying these results to aggregated IBM hardware data, we obtain positive raw-count cycle-product certificates of 0.0812 for CHSH and 0.2178 for Mermin--GHZ, while the nine-context magic-square construction remains uncertified; readout-mitigated values are reported separately as sensitivity estimates. We also analyze a non-Bell quantum-kernel benchmark, where a label-construction variable has measured conditional dependence ηλ(Y)=0.5, above the threshold ηreq=0.375, required to close the reported score gap, and yields perfect classical classification. The framework therefore converts a quantum--classical score separation into a quantitative lower bound on the benchmark-correlated classical information required to explain the score separation.
Quantum machine learning (QML) for network intrusion detection (NIDS) is routinely reported to reach near-perfect accuracy, yet the most rigorous studies find that well-tuned classical models remain competitive, and that apparent quantum gains may be artefacts of classical dimensionality reduction and implicit regularisation rather than genuine quantum effects. We ask not whether a quantum model can post a high accuracy, but how quantum the advantage really is. We present a unified, reproducible QML-IDS benchmark evaluating hybrid variational quantum circuits and quantum-kernel SVMs against five honestly-tuned classical baselines across four standard NIDS datasets (NSL-KDD, UNSW-NB15, CICIDS2017, NF-ToN-IoT-v2) under one leakage-controlled protocol, with an equal-budget feature view, imbalance- and calibration-aware metrics with significance testing, and a simulated NISQ noise sweep. We introduce a quantum-attribution audit (parameter-matched classical controls, a random-feature kernel, and a regularisation sweep) that quantifies how much of any gain is genuinely attributable to the quantum component. Tuned classical models (Random Forest, XGBoost) match or exceed the quantum models on aggregate detection on every dataset, and the audit attributes this to classical preprocessing and regularisation rather than quantum effects. Two advantages survive false-discovery-rate correction: the quantum-kernel SVM out-ranks its direct classical surrogate (a random-feature kernel) on AUPRC and ROC-AUC, and a small four-qubit hybrid out-detects the best classical baseline at the 1% false-positive operating point on the distribution-shifted NSL-KDD task (p = 0.005, BH q = 0.030). Code, seeds, and splits are released; our contribution stands whether quantum wins, ties, or loses.
We present ThylerSpectral-Audit-Q, a three-layer automated diagnostic framework for quantum kernel pathologies, validated across 124 configurations spanning 7 data domains plus a systematic six-family quantum kernel survey: tabular (digits, diabetes, California housing, covtype), clinical (Iris, Wine, Breast Cancer), quantum-native (V0/V1 ZZFeatureMap, V2 IQPFeatureMap), molecular graph (MUTAG, PTC_FM), industrial (semiconductor proxy, Steel Plates Faults, satellite proxy), time series (AR2, ECG5000 via ZZFeatureMap, QHMM, and TSHK kernels). The kernel survey applies six encoding families (PauliFeatureMap, AngleEncoding, AmplitudeEncoding, EfficientSU2, RandomCircuitKernel, QFTFeatureMap) to three tabular benchmark datasets at n ∈ {4, 6, 8}. Contribution 1 — Diagnostic framework. Three sequential layers — exponential concentration (EC) detection (Shannon effective rank ratio r_eff; five-tier spectral taxonomy), dequantization filter (Tang-Chia eigenvalue truncation), and kernel-target alignment evaluation (centered KTA) — combine into a composite PROCEED/CAUTION/ABORT Spectral Health Card. All four primary datasets (breast cancer, make_moons, Iris, Wine) yield ABORT or CAUTION verdicts under ZZFeatureMap. The framework generalizes: IQPFeatureMap reproduces EC_COLLAPSE at n=8 (r_eff=0.943) without recalibration. A data-kernel structural sensitivity is also detected: the same kernel yields LIKELY_DEQUANTIZABLE on molecular graph data (r_eff=0.153) versus CONFIRMED_DEQUANTIZABLE on tabular data (r_eff=0.095) — a distinction invisible to kernel architecture inspection alone. Contribution 2 — Advantage regime, retired at n_train=150 (v19). At n_train=50, Hamming Quantum Kernel (HQK) on quantum-native data produced the paper's only non-ABORT signal: large effect sizes over SVM-Linear on V2 (IQPFeatureMap) data (d=+0.949–1.015; under the corrected resampled t-test for repeated-CV dependence, p_NB=0.0605 for λ=0.5 and p_NB=0.0485 for λ=0.1 — marginal). Because the pre-registered robustness criterion required corrected significance in both λ configurations, a recovery experiment at n_train=150 was pre-registered (exploracion_010) and has now been executed (S052). Result: every V2 effect size reverses sign — λ=0.5: d=−0.215 (p_NB=0.6375, ns); λ=0.1: d=−1.243 (p_NB=0.0189 — a significant disadvantage, HQK now performing worse than SVM-Linear/RBF) — and the pre-registered effect-size-floor control (d≥0.5 in both λ, designed to distinguish gradual collapse from sign reversal) fails in both configurations. The secondary same-architecture V0/V1 arm also reverses sign (d=+0.27→−0.374 vs Linear, ns). Per the pre-registered decision rule, the cross-architecture advantage claim is retired, not restored. This converges with exploracion_012's finding that V6 — a circuit verified diagonal-unitary by construction but structurally distinct from V0/V1/V2's ZZ/IQP coupling — also shows significant disadvantage at n_train=150 (d=−1.10 to −1.13, p_NB<0.05 in both λ): at the matched n_train=150 standard, no HQK configuration tested in this paper shows a robust advantage over classical baselines. The dual concentration bottleneck — global EC (fidelity collapse) and local EC (Pauli-Z observables ⟨Z_i⟩→0 as n increases) — disables both fidelity kernels and projected quantum kernels simultaneously, and this negative result is now the paper's consistent empirical picture rather than a partial exception to it. A complementary negative structural result: exhaustive hyperparameter optimization over ZZFeatureMap (63 grid configurations: γ × reps × entanglement, plus 100-step continuous variational search) on classical time series data (AR2_n4, r_eff=0.2975) finds zero configurations with Δ_kta > 0 in full audit, confirming that quantum-native data is a necessary but not sufficient structural condition for any advantage signal under the full three-layer audit within the ZZFeatureMap family. The D6 kernel survey further shows that K2 (AngleEncoding) achieves Δ_kta>0 on classical tabular data, but is blocked from PROCEED by the dequantization filter, confirming that Layers 1–2 are essential to prevent false PROCEED verdicts. Contribution 3 — Quantum kernel phase diagram. The 124 audited configurations form a quantum kernel phase diagram in (r_eff × Δ_acc × n_qubits) space with two robustly confirmed empirical phases (ABORT, CAUTION) and measurable phase boundaries, plus a third, provisional phase (PROCEED, 7/124 configs) that has not been re-verified at the n_train=150 standard that retired Contribution 2 above. Seven geometric patterns are observable, including a cross-domain discovery: the STRUCTURED_LOW_RANK regime (0.10 < r_eff ≤ 0.35) appears independently in molecular graph data (r_eff ∈ [0.036, 0.312]) and industrial quality-control data (r_eff=0.22), despite no domain relationship — a finding invisible to kernel architecture inspection alone. Contribution 4 — Domain-agnostic spectral classification. A k-nearest-neighbor classifier trained exclusively on spectral audit features achieves F1-macro=1.000 and MCC=1.000 on an external test set of 20 configurations from three entirely unseen domains: molecular graphs, industrial QC, and time series. Random Forest feature importance reveals dataset_type_code=0% — the framework's diagnostic accuracy is domain-invariant by construction. To the best of our knowledge, ThylerSpectral-Audit-Q is the only pre-execution diagnostic tool integrating EC detection, dequantization filtering, and structural alignment evaluation into a single automated pipeline with an empirical multi-domain phase diagram, validated across 124 configurations spanning 7 data domains and a systematic six-family quantum kernel survey.
Quantum kernel estimation on near-term hardware is shot-budgeted: every entry of the kernel Gram matrix is a Bernoulli expectation that must be sampled with a finite number of circuit executions. Recent work on quantum kernel classification has shown that allocating shots non-uniformly across kernel entries, weighted by their downstream task sensitivity, can reduce the shot budget required to reach a target accuracy. We extend this idea to Gaussian process (GP) regression, a setting whose downstream quantities (full-spectrum posterior variance, log-determinant, marginal likelihood) couple to kernel error more tightly than the sign-only outputs of classification. We derive three closed-form pair-level sensitivities predictive coupling ∣αiαj∣, leave-one-out residual, and marginal-likelihood gradient and plug them into a Neyman-style minimum-variance allocation rule. To prevent catastrophic over-concentration when the warm-up sensitivity estimate is itself noisy, we add a high uniform coverage floor justified by a Frobenius lower bound on the missing-entry perturbation. On four UCI benchmarks and two synthetic RBF + Bernoulli controlled studies, the resulting allocator delivers 10--21% test-RMSE improvement over uniform allocation across the moderate-budget regime. The gain transfers (i) to genuine ZZ and Pauli-Z quantum kernels on quantum-natural data (−13--15% at low budget, p<0.05 paired) and (ii) to four downstream tasks (Bayesian quadrature, heteroscedastic regression, hyperparameter learning, multi-output Cokriging). On UCI features embedded into a ZZ kernel the gain disappears, consistent with the exponential-concentration regime where shot allocation has nothing to exploit.