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Bandwidth, Representation Loss, and Temporal Drift in Quantum Kernel Fraud Detection: A Pre-Specified Falsification Study

Mohamed Faisal Sindhi, Hammaz Buksh

Published Oct 13, 2026• 0 citations
Publisher

Abstract

Abstract Quantum kernel results are often reported without holding the input representation, training sample, tuning budget and temporal evaluation protocol fixed against a matched classical kernel. This pre-specified, protocol-locked falsification study uses the Elliptic++ transaction tables (203,769 transactions, 49 time steps) under a locked temporal split (training steps 1–24, validation 25–29, test 30–49 in 4 locked windows). The primary metric is pooled Recall@5%. A frozen full-dimensional gradient-boosting model reached 0.381, and every model, including this one, collapsed in the final window. Graph structure and selective reranking were tested first and falsified. Compressing 182 features to 4, 6 and 8 principal components retained 34%, 43% and 51% of the variance and 64%, 50% and 33% of the full-dimensional model’s pooled Recall@5%. In the primary, default-bandwidth analysis, an entangling fidelity quantum kernel was below the strongest matched classical kernel at 4, 6 and 8 qubits (pooled Recall@5% differences −0.078, −0.203 and −0.146). In a secondary, post hoc bandwidth correction, explicit scale tuning raised the entangling kernel’s Recall@5% by 0.070, 0.121 and 0.109; the corrected kernel remained below the strongest matched classical kernel at 6 and 8 qubits and was statistically unresolved at 4 qubits. The selected scale lay at the lower boundary of the tested grid, and the apparent effect of entanglement depended on bandwidth. No repeatable predictive benefit of the quantum kernel over matched classical kernels was observed in the tested setting; the findings do not extend beyond this dataset, protocol, representation, feature-map family, sample size and bandwidth range.

DOI
10.21203/rs.3.rs-11322513/v1

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Abstract Quantum kernel results are often reported without holding the input representation, training sample, tuning budget and temporal evaluation protocol fixed against a matched classical kernel. This pre-specified, protocol-locked falsification study uses the Elliptic++ transaction tables (203,769 transactions, 49 time steps) under a locked temporal split (training steps 1–24, validation 25–29, test 30–49 in 4 locked windows). The primary metric is pooled Recall@5%. A frozen full-dimensional gradient-boosting model reached 0.381, and every model, including this one, collapsed in the final window. Graph structure and selective reranking were tested first and falsified. Compressing 182 features to 4, 6 and 8 principal components retained 34%, 43% and 51% of the variance and 64%, 50% and 33% of the full-dimensional model’s pooled Recall@5%. In the primary, default-bandwidth analysis, an entangling fidelity quantum kernel was below the strongest matched classical kernel at 4, 6 and 8 qubits (pooled Recall@5% differences −0.078, −0.203 and −0.146). In a secondary, post hoc bandwidth correction, explicit scale tuning raised the entangling kernel’s Recall@5% by 0.070, 0.121 and 0.109; the corrected kernel remained below the strongest matched classical kernel at 6 and 8 qubits and was statistically unresolved at 4 qubits. The selected scale lay at the lower boundary of the tested grid, and the apparent effect of entanglement depended on bandwidth. No repeatable predictive benefit of the quantum kernel over matched classical kernels was observed in the tested setting; the findings do not extend beyond this dataset, protocol, representation, feature-map family, sample size and bandwidth range.
Quantum kernel methods are the most concrete near-term proposal for quantum machine learning on classical data, yet published benchmarks disagree on whether they outperform tuned classical kernels, and the disagreement cannot be resolved from the literature because the comparisons are not protocol-controlled. We argue that the obstacle is one of measurement, not theory: the usual setup fixes the quantum feature map's data scaling while grid-searching the classical kernel's hyperparameters, recomputes nothing per fold, and reports cost in simulator time. We therefore treat the comparison itself as the object of study and impose three controls. The bandwidth is tuned on the same grid budget as the classical γγγ, the kernel is recomputed inside every fold from fold-fitted preprocessing, and cost is counted in hardware circuit evaluations. On top of these we run a factorial design of 324 cells in which dimensionality, training size, class separability and data structure are explicit covariates, together with four standard datasets, a shots-versus-gate-noise ablation, and a cost sweep. The dominant effect we measure is not quantum: tuning the feature map's bandwidth is worth 0.120 accuracy on synthetic data and 0.339 on real data, exceeding every quantum-classical difference we observe. Tuned quantum kernels are then statistically indistinguishable from a tuned RBF on all four real datasets. The advantage on synthetic data is confined almost entirely to data generated by the feature map itself, and it shrinks with dimensionality (-0.0045 per qubit) while growing with sample size. Finite sampling costs an order of magnitude more accuracy than gate and readout noise, and a fidelity kernel needs 5×1075\times10^{7}5×107 circuits at n = 10,000. Protocol variance is thus sufficient to explain the field's contradictory conclusions.
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=0.194p=0.194p=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.
Do quantum kernels improve cross-sectional stock return prediction? We run a controlled horse race on the Chinese A-share market in which a quantum fidelity kernel, a projected quantum kernel, and a classical RBF control share identical training subsamples, solver, and tuning budgets, so that only the kernel is exchanged. On the main evaluation -- a point-in-time universe and 170 walk-forward windows (2012-2025) -- no quantum advantage exists: the fidelity kernel is indistinguishable from its RBF control (ΔΔΔIC =+0.005=+0.005=+0.005, p=0.42p=0.42p=0.42), and a 2×22\times22×2 design crossing kernel type with training budget (a Nystrom extension to the full ~38,000-observation windows) shows quantum kernels matching, but never beating, equal-budget linear models; after family-wise correction no pairwise difference among eleven models is significant, with point estimates favoring penalized linear regressions throughout. We then document how the opposite conclusion arises: a 60-window evaluation on a universe screened with full-sample information makes the same quantum kernel appear dominant on stability criteria and significantly better than neural baselines. Interaction characteristics from the anomalies literature help nothing, quantum or classical; a widened bandwidth grid reveals an interior optimum rather than the near-classical endpoint a coarse grid suggests; and the geometric difference, while large throughout (g≫1g \gg 1g≫1), does not predict out-of-sample gains (ρ=−0.20ρ=-0.20ρ=−0.20). We propose protocol standards -- kernel-swap controls, budget-equalized comparisons, point-in-time universes, and multiplicity-robust inference -- for empirical claims of quantum advantage in finance.
Detecting credit card fraud is notoriously difficult because fraudulent charges make up less than 0.2% of total transactions. Quantum Machine Learning (QML), particularly Quantum Kernel Support Vector Machines (QSVM), promises richer feature representations by embedding classical data into high-dimensional Hilbert spaces. However, whether this theoretical advantage holds up when managing real-world financial data bottlenecks remains unclear. We designed a controlled benchmark comparing three quantum encodings, Angle, ZZFeatureMap, and IQP against classical models while keeping sample sizes, feature counts, and scaling strictly matched. To handle class skew without corrupting quantum state overlaps, we embedded synthetic minority oversampling (SMOTE) directly into the quantum Gram matrix workflow, raising PR-AUC scores by roughly +0.04 across feature maps. When trained on the full European credit card dataset with 30 features, classical baselines reached a top PR-AUC of 0.983. However, restricting classical models to match QSVM hardware constraints (500 samples, 4 PCA features) dropped their PR-AUC to 0.750. This puts our best quantum result 0.730 PR-AUC using IQP encoding on 150 samples into realistic context. Testing on physical quantum hardware reduced performance further to 0.62 due to CNOT gate errors and thermal noise. Overall, our findings pinpoint two main operational bottlenecks for near-term quantum kernels: the scaling of Gram matrix evaluation and heavy information loss from squeezing features onto small qubit registers.
We benchmarked quantum kernel kkk-means against classical clustering for credit-card fraud detection on real transaction data, at up to \MaxQubits{} qubits, under a protocol with separated selection and reporting data and matched search budgets. We find no robust quantum advantage: the sign of the difference depends on register size, all effect sizes are below 0.0130.0130.013 ARI, and the single significant advantage we observe is fully explained by the number of configurations searched. We further show that ordinary hyperparameter choices move performance by considerably more than the quantum kernel does, that additional qubits degrade rather than improve performance through kernel concentration, and that the clustering framing itself fails at realistic class imbalance though kernel-based anomaly scoring does not. We regard the methodological contribution as the more durable one. The search-budget ablation in particular is inexpensive and, in our case, decisive: it converted a statistically significant advantage into a procedural artefact. We would encourage its routine use.
Quantum kernel methods are promising for near-term quantum machine learning, but their training costs are driven by the quadratic scaling of Gram-matrix construction and the measurement cost of estimating individual kernel values. In this work, we investigate one-class anomaly detection as a resource-efficient operating regime for training non-variational quantum kernel models. Using the ULB Credit Card Fraud Detection dataset, we evaluate three quantum feature maps across training-set sizes and qubit counts. Power-law saturation models reveal strong diminishing returns with increasing training data, with 500-sample models retaining approximately 90--93\% of their fitted asymptotic average precision (AP). We further observe no severe exponential concentration among the evaluated feature maps over the investigated qubit range, thereby avoiding the exponentially increasing measurement requirements associated with that regime. Finally, Nyström approximation reduces kernel construction from O(N2)\mathcal{O}(N^2)O(N2) to O(Nm)\mathcal{O}(Nm)O(Nm) evaluations, with QSVR retaining 94--97\% of its exact-kernel AP using only five landmarks. For ZZ-QSVR, downsampling from 4,000 to 500 training samples and applying a five-landmark approximation decreases the number of required kernel evaluations from approximately 8.08.08.0 million to 2,4852,4852,485, a reduction of more than 3,200-fold, while AP decreases from 0.8120.8120.812 to 0.7370.7370.737. Under the minimum IonQ pricing assumption considered here, this corresponds to an illustrative reduction in quantum kernel training cost from approximately $1.34 billion to $417{,}480. These results demonstrate that training-set reduction and low-rank approximation can substantially reduce the resources required to train non-variational quantum kernel anomaly detectors while retaining meaningful anomaly-discrimination performance.