Provable and scalable quantum Gaussian processes for quantum learning

TL;DR

This paper introduces quantum Gaussian processes, a Bayesian framework for quantum data learning, leveraging quantum process structures to enable scalable, interpretable quantum machine learning methods.

Contribution

The authors develop quantum Gaussian processes based on quantum stochastic processes, proving their scalability with matchgate evolutions and demonstrating practical quantum learning applications.

Findings

Quantum Gaussian processes enable regression, classification, and optimization on quantum data.

Matchgate evolutions produce provable, scalable quantum Gaussian processes.

The framework achieves accurate extrapolation and efficient quantum sensing.

Abstract

Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally suited to quantum data. To address this, 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 key ingredient in this framework is sufficient knowledge of a quantum process's structure and symmetries to define an informative prior through its corresponding quantum kernel, effectively injecting a strong, physics-informed inductive bias into the learning model. We then prove that matchgate, or free-fermionic, evolutions give rise to provable and scalable quantum Gaussian processes, providing the first family in our framework where the unknown unitary acts non-trivially on all qubits. Finally, we demonstrate accurate long-range extrapolation, phase-diagram learning in many-body systems, and sample-efficient Bayesian optimization in a quantum sensing task. Our results identify quantum Gaussian processes as a promising route toward simpler and more structured forms of quantum learning.