Physics-inspired inductive biases for classical and quantum machine learning

This thesis investigates how principles from physics can serve as inductive biases that make learning and optimization more tractable in machine learning and quantum computing. Physical structure - encoded in Hamiltonians, physics-inspired dynamics, circuit architectures, and measurement protocols - constrains the hypothesis class, enabling learning under limited computational and data budgets in high-dimensional settings. The thesis presents four case studies showing how these physics-inspired inductive biases can be incorporated into both classical and quantum models. First, quantum diffusion models are introduced as generative models for quantum states. A Markovian noising process, motivated by statistical physics, defines the forward dynamics, while parameterized quantum circuits implement the reverse dynamics. Second, a Potts-model Hamiltonian is used to formulate a graph-coloring objective, leading to a physics-informed neural architecture that generalizes beyond the training distribution. Third, parameterized quantum circuits and hybrid classical-quantum models are evaluated for an anomaly detection task in highly imbalanced classical transaction data, using circuit structure as an additional inductive bias. Fourth, a data-driven classical-shadow method is developed, in which a neural network maps shadow snapshots to observable expectation values. This work fits into the broader effort of quantum device certification. Overall, the results show that physics-inspired inductive biases are a robust lever for resource-efficient learning, while NISQ-era quantum resources provide modest task- and metric-dependent benefits rather than a consistent advantage over classical baselines.