Where might quantum regression models fit? A benchmark across tides, wind, soccer and galaxy redshifts

Variational circuits that re-upload their inputs compute truncated Fourier series, which suggests they might be well suited to data whose inputs are genuinely periodic. We test this idea on four public regression problems that span the range from periodic to purely tabular inputs: tidal water levels, wind-turbine power, the probability that a soccer shot is scored, and galaxy redshift from photometry. A re-uploading circuit and a fidelity quantum kernel are compared with five classical learners and with the methods practitioners in each field use, under an equal hyperparameter budget, structure-aware data splits and training sets of 50 to 1000 points, for 850 runs in total. No quantum model outperforms the best classical or domain method on any dataset at any training size. The quantum kernel with an angle feature map is nonetheless competitive on the tidal and redshift problems, whereas the IQP feature map is consistently rejected on periodic inputs because its product terms break periodicity. A spectral analysis of the tidal problem shows that the frequencies available to a single-layer circuit already permit a test R² of 0.932, on par with the best classical model. The variational model's shortfall therefore stems from optimization and from the restricted set of Fourier coefficients the ansatz can reach, not from its frequency spectrum, while deeper circuits introduce frequencies the data do not contain and train less well.