Distributed Quantum Gaussian Processes for Multi-Agent Systems

Gaussian processes (GPs) provide a flexible framework for learning unknown functions from noisy measurements while quantifying predictive uncertainty, making them well suited for estimation in multi-agent systems. However, when measurements are collected by multiple agents, maintaining a unified GP model without centralized processing requires efficient distributed algorithms that can operate using local measurements and communication with neighboring agents. In this work, we develop two distributed recursive GP (RGP) algorithms for multi-output GP regression: ADMM-RGP and PDMM-RGP. We analyze the stability and convergence of both algorithms and develop parameter selection strategies to accelerate convergence, thus reducing the communication burden. The proposed methods are validated on a real-world multi-output wind dataset, and their convergence behavior is examined across communication graphs with varying connectivity. Numerical experiments demonstrate that ADMM-RGP and PDMM-RGP can significantly reduce communication relative to the state of the art, while maintaining comparable estimation accuracy and network-wide consensus.

Reinforcement learning (RL) is one of the most practical ways to learn from real-life use-cases. Motivated from the cognitive methods used by humans makes it a widely acceptable strategy in the field of artificial intelligence. Most of the environments used for RL are often high-dimensional, and traditional RL algorithms becomes computationally expensive and challenging to effectively learn from such systems. Recent advancements in practical demonstration of quantum computing (QC) theories, such as compact encoding, enhanced representation and learning algorithms, random sampling, or the inherent stochastic nature of quantum systems, have opened up new directions to tackle these challenges. Quantum reinforcement learning (QRL) is seeking significant traction over the past few years. However, the current state of quantum hardware is not enough to cater for such high-dimensional environments with complex multi-agent setup. To tackle this issue, we propose a distributed framework for QRL where multiple agents learn independently, distributing the load of joint training from individual machines. Our method works well for environments with disjoint sets of action and observation spaces, but can also be extended to other systems with reasonable approximations. We analyze the proposed method on cooperative-pong environment and our results indicate ~10% improvement from other distribution strategies, and ~5% improvement from classical models of policy representation.

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.