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This study identifies a fundamental structural barrier, termed the "Fourier wall," that prevents quantum machine learning from outperforming classical models on standard tabular datasets. The authors introduce SPECTRA, a certification framework to distinguish between trivial benchmarks and rare cases where genuine quantum advantage is theoretically possible due to specific spectral properties in the data. By validating this with real-world energy grid simulations involving interacting quantum processes, the research provides a practical roadmap for engineering problems that can truly leverage near-term quantum hardware.
The Fourier Wall: Why Public Tabular Datasets Refuse Quantum Advantage, and a Certified Recipe for Where It Lives
arXiv:2607.15815v1 Announce Type: new Abstract: 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.
Abstract: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.
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
arXiv:2607.15815 [quant-ph]
(or arXiv:2607.15815v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.15815 arXiv-issued DOI via DataCite (pending registration)
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