Quantum Kernel k-Means for Credit-Card Fraud Detection:A Controlled Benchmark on Real Transaction Data

We benchmarked quantum kernel $k$-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 $0.013$ 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.