Periodic Readout Induces a First-Order Generalization Transition in a Quantum Perceptron

arXiv:2611.10887v1 Announce Type: new Abstract: Variational quantum classifiers can generate highly structured decision boundaries through the Fourier dependence of observable expectation values on circuit parameters. We show that expressivity can come at a sharp statistical cost, by considering a quantum perceptron whose readout is the simplest periodic classifier, namely a square-wave function of the weighted inputs, and determine its typical generalization in the thermodynamic limit using a teacher-student replica-symmetric theory. Above a critical oscillation frequency, increasing the training load induces a first-order transition from weakly to strongly teacher-aligned phases, resulting in a discontinuous improvement in generalization.