Distributed Quantum Gaussian Processes for Multi-Agent Systems

2026-02-16

AI Summary

This work addresses the limitations of classical Gaussian processes in modeling non-stationary, high-dimensional data due to the restricted expressiveness of conventional kernel functions. To overcome this, we propose a distributed quantum Gaussian process model that embeds data into a high-dimensional Hilbert space to enhance representational capacity, and for the first time integrates quantum Gaussian processes with multi-agent distributed optimization. We develop a Riemannian DR-ADMM algorithm tailored to non-Euclidean geometric constraints, enabling a scalable hybrid quantum–classical modeling framework. Experiments on real-world non-stationary terrain data from NASA and synthetic quantum datasets demonstrate that the proposed method significantly outperforms existing approaches and validates the potential acceleration advantage of quantum hardware in Gaussian process inference and distributed optimization.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Gaussian Processes
• Quantum Computing
• Multi-Agent Systems
• Scalability
• Non-Euclidean Optimization

Innovation

• Distributed Quantum Gaussian Process
• DR-ADMM
• Quantum Kernel Embedding
• Multi-Agent Consensus Optimization
• Hilbert Space Embedding