Distributed Quantum Gaussian Processes for Multi-Agent Systems
This work addresses scalability and expressivity limitations in Gaussian Processes for multi-agent systems, offering a quantum-enhanced approach that is incremental but shows potential computational speedups.
The paper tackles the limited expressivity of classical Gaussian Process kernels in large-scale domains by proposing a Distributed Quantum Gaussian Process method for multi-agent systems, achieving enhanced modeling capabilities through a distributed consensus Riemannian ADMM algorithm and demonstrating efficacy on real-world and synthetic datasets via quantum simulator experiments.
Gaussian Processes (GPs) are a powerful tool for probabilistic modeling, but their performance is often constrained in complex, largescale real-world domains due to the limited expressivity of classical kernels. Quantum computing offers the potential to overcome this limitation by embedding data into exponentially large Hilbert spaces, capturing complex correlations that remain inaccessible to classical computing approaches. In this paper, we propose a Distributed Quantum Gaussian Process (DQGP) method in a multiagent setting to enhance modeling capabilities and scalability. To address the challenging non-Euclidean optimization problem, we develop a Distributed consensus Riemannian Alternating Direction Method of Multipliers (DR-ADMM) algorithm that aggregates local agent models into a global model. We evaluate the efficacy of our method through numerical experiments conducted on a quantum simulator in classical hardware. We use real-world, non-stationary elevation datasets of NASA's Shuttle Radar Topography Mission and synthetic datasets generated by Quantum Gaussian Processes. Beyond modeling advantages, our framework highlights potential computational speedups that quantum hardware may provide, particularly in Gaussian processes and distributed optimization.