Can quantum communication speed up distributed computation?

Michael Elkin, Hartmut Klauck, Danupon Nanongkai, Gopal Pandurangan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

32 Scopus citations

Abstract

The focus of this paper is on quantum distributed computation, where we investigate whether quantum communication can help in speeding up distributed network algorithms. Our main result is that for certain fundamental network problems such as minimum spanning tree, minimum cut, and shortest paths, quantum communication does not help in substantially speeding up distributed algorithms for these problems compared to the classical setting. In order to obtain this result, we extend the technique of Das Sarma et al. [SICOMP 2012] to obtain a uniform approach to prove non-trivial lower bounds for quantum distributed algorithms for several graph optimization (both exact and approximate versions) as well as verification problems, some of which are new even in the classical setting, e.g. tight randomized lower bounds for Hamiltonian cycle and spanning tree verification, answering an open problem of Das Sarma et al., and a lower bound in terms of the weight aspect ratio, matching the upper bounds of Elkin [STOC 2004]. Our approach introduces the Server model and Quantum, Simulation Theorem, which together provide a connection between distributed algorithms and communication complexity. The Server model is the standard twoparty communication complexity model augmented with additional power; yet, most of the hardness in the two-party model is carried over to this new model. The Quantum Simulation Theorem carries this hardness further to quantum distributed computing. Our techniques, except the proof of the hardness in the Server model, require very little knowledge in quantum computing, and this can help overcoming a usual impediment in proving bounds on quantum distributed algorithms. In particular, if one can prove a lower bound for distributed algorithms for a certain problem using the technique of Das Sarma et al., it is likely that such lower bound can be extended to the quantum setting using tools provided in this paper and without the need of knowledge in quantum computing. distributed computing; graph algorithms; quantum communication; time complexity; lower bound, CONGEST model

Original languageEnglish
Title of host publicationPODC 2014 - Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages166-175
Number of pages10
ISBN (Print)9781450329446
DOIs
StatePublished - 1 Jan 2014
Event2014 ACM Symposium on Principles of Distributed Computing, PODC 2014 - Paris, France
Duration: 15 Jul 201418 Jul 2014

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference2014 ACM Symposium on Principles of Distributed Computing, PODC 2014
Country/TerritoryFrance
CityParis
Period15/07/1418/07/14

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

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