Speaker
Description
Quantum machine learning has become increasingly popular, but despite tremendous efforts, some of its central issues like trainability, scalability, poor local minima, interpretability, and reliable generalization from limited quantum data still remain. This motivates a different organizing principle for quantum learning, where the model is not chosen as a flexible ansatz, but is instead dictated by the structure and symmetries of the underlying quantum process. Here we introduce quantum Gaussian processes, a Bayesian framework for learning from quantum systems through priors over unknown quantum transformations. We show that, under suitable conditions, unitary quantum stochastic processes define Gaussian processes, thereby enabling regression, classification, and Bayesian optimization directly on quantum data. The corresponding quantum kernel is not a heuristic similarity measure, but the covariance induced by prior knowledge of the process and measurement, injecting a physics-informed inductive bias into the learning model. Our main theoretical result proves that matchgate, or free-fermionic, evolutions give rise to provable and scalable quantum Gaussian processes, yielding the first family in our framework where the unknown unitary acts non-trivially on all qubits. We demonstrate accurate long-range extrapolation, phase-diagram learning in many-body systems, and sample-efficient Bayesian optimization in a quantum sensing task. These results establish quantum Gaussian processes as a principled route toward structured, uncertainty-aware, and scalable quantum learning. This extended abstract summarizes work available as an arXiv preprint: https://arxiv.org/abs/2605.00099
| Topic | Theoretical foundations of quantum learning |
|---|---|
| Additional Topic | Quantum kernel methods and their applications |