用量子计算提升多智能体系统的概率建模能力
Distributed Quantum Gaussian Processes for Multi-Agent Systems
- 设计分布式量子高斯过程，利用量子态扩展数据表达能力
- 通过分布式黎曼优化算法实现多智能体模型聚合
- 在真实地形与合成数据上验证性能，展现量子加速潜力
高斯过程（GPs）是强大的概率建模工具，但在复杂大规模现实场景中受限于经典核函数的表达能力。量子计算可通过将数据嵌入指数级大的希尔伯特空间，捕捉经典方法无法处理的复杂相关性。本文提出一种多智能体环境下的分布式量子高斯过程（DQGP）方法，以增强建模能力和可扩展性。针对非欧几里得优化难题，设计了分布式共识黎曼交替方向乘子法（DR-ADMM）算法，实现本地模型向全局模型的聚合。通过在经典硬件上的量子模拟器进行数值实验，使用美国宇航局航天雷达地形测绘任务的真实非平稳高程数据集及量子高斯过程生成的合成数据集评估方法有效性。除建模优势外，该框架还揭示了量子硬件在高斯过程与分布式优化中的潜在计算加速能力。
原文摘要 · Abstract (English)
Gaussian Processes (GPs) are a powerful tool for probabilistic modeling, but their performance is often constrained in complex, large-scale 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 multi-agent 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.
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