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Distributed Quantum Gaussian Processes for Multi-Agent Systems

Meet Gandhi, George P. Kontoudis

TL;DR

A Distributed Quantum Gaussian Process (DQGP) method in a multiagent setting to enhance modeling capabilities and scalability and a Distributed consensus Riemannian Alternating Direction Method of Multipliers (DR-ADMM) algorithm that aggregates local agent models into a global model.

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.

Distributed Quantum Gaussian Processes for Multi-Agent Systems

TL;DR

A Distributed Quantum Gaussian Process (DQGP) method in a multiagent setting to enhance modeling capabilities and scalability and a Distributed consensus Riemannian Alternating Direction Method of Multipliers (DR-ADMM) algorithm that aggregates local agent models into a global model.

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.
Paper Structure (17 sections, 1 theorem, 19 equations, 4 figures, 2 tables, 2 algorithms)

This paper contains 17 sections, 1 theorem, 19 equations, 4 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Classical Gaussian Processes (GPs)
  4. Function-Space View of Gaussian Processes
  5. Quantum Gaussian Processes (QGPs)
  6. Distributed Gaussian Processes (DGPs)
  7. Problem Statement
  8. Proposed Methodology
  9. Distributed consensus Riemannian ADMM
  10. Manifold Definition and Operations
  11. Quantum Gaussian Process Loss Function
  12. Distributed consensus Riemannian ADMM (DR-ADMM)
  13. Distributed Quantum Gaussian Process
  14. Quantum Encoding Circuits
  15. Quantum Kernels
  16. ...and 2 more sections

Key Result

Theorem 1

Let the negative marginal log-likelihood functions $\mathcal{L}_{Q,m}: \mathcal{T}^p \to \mathbb{R}$ be $L_p$-smooth $\forall m \in [1,M]$ on the torus manifold $\mathcal{T}^p$ with bounded projections $\Pi_{\mathcal{T}}(\cdot)$, and assume the existence of a uniform bound $C < \infty$ such that $\|

Figures (4)

  • Figure 1: Distributed Quantum Gaussian Process (DQGP): A hybrid classical-quantum framework for multi-agent systems.
  • Figure 2: The structure of the proposed DQGP with 4 agents. The consensus algorithm is the proposed DR-ADMM optimization.
  • Figure 3: Performance of DQGP (green) with the SRTM dataset, compared to Full-GP williams2006gaussian, FACT-GP deisenroth2015distributed, and apx-GP xie2019distributed. For N43W080 and N47W124, we have excluded visualizing the apxGP results (worst performance) in NLPD for better readability.
  • Figure 4: Performance of DQGP (green) on 2D QGP prior dataset, compared to Full-GP williams2006gaussian, FACT-GP deisenroth2015distributed, and apx-GP xie2019distributed.

Theorems & Definitions (1)

  • Theorem 1: Convergence of DR-ADMM