Provable and scalable quantum Gaussian processes for quantum learning

2026-04-30

AI Summary

Existing learning frameworks struggle to simultaneously achieve interpretability, scalability, and natural compatibility with quantum data. This work proposes Quantum Gaussian Processes (QGPs), establishing the first quantum learning framework that integrates physically informed inductive biases with Bayesian inference capabilities. By introducing a provably scalable prior over unknown unitary operators—derived from the evolution of matchgate (free-fermion) circuits—the method leverages symmetry-guided quantum kernel design to model nontrivial actions across all qubits. The approach demonstrates superior performance in learning many-body phase diagrams, long-range extrapolation, and sample-efficient Bayesian optimization for quantum sensing tasks.

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.

Problem

• quantum machine learning
• learning framework
• quantum data
• scalability
• interpretability

Innovation

• quantum Gaussian processes
• Bayesian learning
• quantum kernel
• matchgate circuits
• physics-informed priors