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.

翻译：高斯过程是一种强大的概率建模工具，但其性能在复杂、大规模的实际应用领域中常受限于经典核函数的表达能力。量子计算通过将数据嵌入指数级大的希尔伯特空间，有望突破这一限制，从而捕捉经典计算方法无法触及的复杂相关性。本文提出了一种多智能体环境下的分布式量子高斯过程方法，以增强建模能力与可扩展性。针对具有挑战性的非欧几里得优化问题，我们开发了一种分布式共识黎曼交替方向乘子法算法，将各局部智能体模型聚合为全局模型。我们通过在经典硬件上运行的量子模拟器进行数值实验，评估了所提方法的有效性。实验使用了NASA航天飞机雷达地形任务获取的真实非平稳高程数据集，以及由量子高斯过程生成的合成数据集。除了建模优势外，我们的框架还凸显了量子硬件可能带来的潜在计算加速，特别是在高斯过程与分布式优化方面。