On the Limits of Distributed Quantum Computing

2025-03-14

AI Summary

This work investigates the fundamental capabilities and limitations of quantum computation in purely distance-constrained (i.e., bandwidth-unconstrained) distributed networks, focusing on the LOCAL model and its quantum extension, quantum-LOCAL. Using a unifying framework that integrates distributed computing theory, quantum query and communication complexity analysis, and lower-bound techniques for graph problems, the paper establishes the first rigorous characterization of intrinsic constraints on distributed quantum computation under distance bounds. Key contributions include: (i) proving that classic LOCAL-solvable problems—such as graph coloring and maximal matching—admit no quantum speedup in the quantum-LOCAL model; (ii) identifying inherent bottlenecks and asymptotic capability ceilings of quantum-LOCAL relative to classical LOCAL; and (iii) precisely delineating the design frontier for quantum distributed algorithms, while synthesizing several critical open questions.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Blockchains and distributed ledgers

Abstract

Quantum advantage is well-established in centralized computing, where quantum algorithms can solve certain problems exponentially faster than classical ones. In the distributed setting, significant progress has been made in bandwidth-limited networks, where quantum distributed networks have shown computational advantages over classical counterparts. However, the potential of quantum computing in networks that are constrained only by large distances is not yet understood. We focus on the LOCAL model of computation (Linial, FOCS 1987), a distributed computational model where computational power and communication bandwidth are unconstrained, and its quantum generalization. In this brief survey, we summarize recent progress on the quantum-LOCAL model outlining its limitations with respect to its classical counterpart: we discuss emerging techniques, and highlight open research questions that could guide future efforts in the field.

Problem

• Explores quantum computing limits in distributed networks
• Compares quantum-LOCAL model with classical distributed computing
• Identifies open research questions in quantum distributed computing

Innovation

• Explores quantum-LOCAL model in distributed computing
• Compares quantum and classical computational limitations
• Highlights open research questions for future studies