Across public tabular benchmarks, quantum machine-learning (QML) models usually lose to carefully tuned classical baselines. We argue that this is a structural property of the datasets rather than merely a limitation of current models. Because an angle-encoded quantum neural network is a partial Fourier series, a genuine advantage can arise only when the target spectrum is simultaneously off-grid, of interaction order at least three, high-frequency, supported by near-independent features, and dense beyond practical enumeration. We call the failure to satisfy these conditions the Fourier wall. We operationalize the conditions as SPECTRA, a two-tier certificate: a simulator-free structural screen followed by a decisive comparison between a matched quantum model and five tuned classical twins using paired-bootstrap confidence bounds. On industrial smart-meter data, SPECTRA correctly refuses the real peak-load target, for which gradient-boosted trees reach a held-out ROC-AUC of 0.999. On the same real energy phases with labels generated by an interacting quantum process, the dynamics-matched quantum model reaches 0.994 versus 0.699 for the best generic classical baseline, and collapses to chance when its interaction couplings are ablated. An exact classical simulator ties the quantum model at small width but incurs measured exponential evaluation cost, with an estimated hardware crossover near 13-19 sites. These results provide a practical recipe for identifying, engineering, and deploying quantum-advantage candidates in tabular data.
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16 pages, 10 figures, 2 tables, and 2 algorithms. The certified positive result uses real energy covariates with a quantum-process-generated label; the real operational target is refused
Across public tabular benchmarks, quantum machine-learning (QML) models usually lose to carefully tuned classical baselines. We argue that this is a structural property of the datasets rather than merely a limitation of current models. Because an angle-encoded quantum neural network is a partial Fourier series, a genuine advantage can arise only when the target spectrum is simultaneously off-grid, of interaction order at least three, high-frequency, supported by near-independent features, and dense beyond practical enumeration. We call the failure to satisfy these conditions the Fourier wall. We operationalize the conditions as SPECTRA, a two-tier certificate: a simulator-free structural screen followed by a decisive comparison between a matched quantum model and five tuned classical twins using paired-bootstrap confidence bounds. On industrial smart-meter data, SPECTRA correctly refuses the real peak-load target, for which gradient-boosted trees reach a held-out ROC-AUC of 0.999. On the same real energy phases with labels generated by an interacting quantum process, the dynamics-matched quantum model reaches 0.994 versus 0.699 for the best generic classical baseline, and collapses to chance when its interaction couplings are ablated. An exact classical simulator ties the quantum model at small width but incurs measured exponential evaluation cost, with an estimated hardware crossover near 13-19 sites. These results provide a practical recipe for identifying, engineering, and deploying quantum-advantage candidates in tabular data.
Quantum machine learning (QML) holds promise for pattern recognition, optimization, and data analysis, but the conditions under which it can outperform classical methods remain unclear. We propose data complexity--the structural, statistical, algorithmic, and topological richness of a dataset--as a central axis for stating such conditions, and test the resulting framework under a pre-specified benchmark. The central predictive claim fails. A composite complexity measure does not predict the budget-matched quantum edge across 27 datasets in leave-one-dataset-out validation (pooled R^2=-0.32, versus a pre-specified threshold of 0.4). The failure is strongly coupled to the classical baseline: against logistic regression, the selector reaches R^2=+0.13 and the parity family wins 17% of cells, whereas against the best of six standard classical models performance falls to R^2=-0.94, with parity winning only 1%. The apparent signal therefore tracks classical model error rather than a robust quantum contribution. The tested encoding and reduction procedures further leave little nonlinear headroom for the downstream model to exploit; gradient boosting matches a linear probe across the tested widths. The null is also constrained by the regime: quantum performance is at chance in 81.5% of cells. Yet a deliberately constructed quantum-signature control produces a +0.42 edge under a structure-aware measurement, while generic models required to learn that structure remain near chance. Thus the null result is not evidence that quantum-sensitive structure cannot exist. Rather, in the tested regime, data complexity alone does not predict quantum advantage: the observable edge depends jointly on the classical baseline, accessible data structure, representation and model headroom, and whether quantum-sensitive structure is accessible to the measurement.
For quantum machine learning, the exact boundary between classical and quantum advantage is still poorly understood. Direct comparison between quantum neural networks (QNNs) and existing classical models, which encompass fundamentally different function classes, often fails to provide broader insight into the difference between the two. Inspired by the techniques of Neural Quantum States and Random Fourier Features, this work introduces Neural Fourier Surrogates (NFS), a stochastic classical neural network architecture for efficiently learning coefficients over the same finite Fourier series support as quantum neural networks. Testing on a selection of tabular benchmark datasets, we find that NFS is an effective classifier architecture broadly competitive with established classical baselines, including a comparable Random Fourier Features model, and possessing comparable performance to data-reuploading QNNs; combined with additional analysis comparing the learned Fourier spectra of QNNs and NFS on synthetic data, these results establish NFS as a natural classical baseline for evaluating QNN performance.
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.
Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed data-encoding map. Amplitude, angle, and basis encoding are evaluated as deterministic feature maps for classical supervised learning under matched output dimensionality and strong classical controls. The benchmark compares these encodings against raw linear models, random Fourier features, polynomial features, PCA, RBF SVMs, and shallow neural networks across diverse classical datasets. Rather than treating performance as a single endpoint, we analyze the geometry of each representation through effective rank, condition number, centered kernel alignment, predictive performance, and practical overhead. The resulting picture is mechanistic: amplitude encoding can remove magnitude information through unit-sphere normalization, angle encoding can become geometrically redundant with raw linear features, and basis encoding can impose a binary Hamming geometry that is poorly aligned with smooth decision structure. These findings do not argue against quantum computation, however, they show that fixed quantum-inspired encoding geometry alone is not a reliable source of machine-learning advantage on classical data.
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.
Abstract Quantum-inspired (QI) optimizers are increasingly proposed as alternatives to classical gradient-based training, yet are frequently benchmarked through classical stand-ins rather than themselves. Across tabular, vision, and language tasks we evaluate three classes: direct implementations of published update rules (Spall’s SPSA; quantum-behaved particle swarm optimization, QPSO, adapted to stochastic minibatches), a documented classical analog of quantum natural gradient (an NGD-style diagonal second-moment preconditioner), and the hyperparameter-control configurations under which such methods are often reported. The gap between these classes is our central result: on the tabular benchmark the hyperparameter control trains with the classical baselines while the direct algorithms fall ≈ 10–24 points below it, and on CIFAR-10/ResNet18, where v1’s “SPSA” arm was a learning-rate-scaled Adam, Adam itself stands ≈ 59 points above genuine SPSA. The QPSO adaptation stays at chance on LSTM tasks a legacy “QPSO” proxy solves at 79–81%, at 18–38 × Adam’s cost there and up to 74 × on the small CV model. A seed-paired 2×2 factorial on RoBERTa identifies the smaller learning rate as the dominant observed component of the earlier “QNG advantage” ( +0.50 points at the dataset level); with only three datasets, modified Hartung–Knapp uncertainty spans zero. The configured NGD arm shows no detectable advantage over a learning-rate-matched AdamW (descriptive pooled p=0.23 ) at 6– 7% extra cost, and on ResNet18 its trained endpoints have larger dominant-curvature estimates than the Adam family’s. Headline comparisons use five seeds, paired tests, Holm correction, and stated detection limits. We conclude with an auditing taxonomy (direct algorithm / analog / hyperparameter control): within the arms, protocols, and scales evaluated, no advantage attributable to a QI mechanism is detected after these controls.