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What Can Be Observed Locally?

Round-Based Models for Quantum Distributed Computing

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Distributed Computing (DISC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5805))

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Abstract

We consider the question of locality in distributed computing in the context of quantum information. Specifically, we focus on the round complexity of quantum distributed algorithms, with no bounds imposed on local computational power or on the bit size of messages. Linial’s \(\mathcal{LOCAL}\) model of a distributed system is augmented through two types of quantum extensions: (1) initialization of the system in a quantum entangled state, and/or (2) application of quantum communication channels. For both types of extensions, we discuss proof-of-concept examples of distributed problems whose round complexity is in fact reduced through genuinely quantum effects. Nevertheless, we show that even such quantum variants of the \(\mathcal{LOCAL}\) model have non-trivial limitations, captured by a very simple (purely probabilistic) notion which we call “physical locality” (\(\varphi\textrm{\upshape -}\mathcal{LOCAL}\)). While this is strictly weaker than the “computational locality” of the classical \(\mathcal{LOCAL}\) model, it nevertheless leads to a generic view-based analysis technique for constructing lower bounds on round complexity. It turns out that the best currently known lower time bounds for many distributed combinatorial optimization problems, such as Maximal Independent Set, bounds cannot be broken by applying quantum processing, in any conceivable way.

Supported by the ANR project “ALADDIN”, by the INRIA équipe-project “CÉPAGE”, and by the KBN Grant 4 T11C 047 25.

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Author information

Authors and Affiliations

  1. LaBRI, University of Bordeaux, France

    Cyril Gavoille & Adrian Kosowski

  2. Dept of Algorithms and System Modeling, Gdańsk University of Technology, Poland

    Adrian Kosowski

  3. Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Poland

    Marcin Markiewicz

Authors
  1. Cyril Gavoille
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  2. Adrian Kosowski
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  3. Marcin Markiewicz
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Idit Keidar

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Gavoille, C., Kosowski, A., Markiewicz, M. (2009). What Can Be Observed Locally?. In: Keidar, I. (eds) Distributed Computing. DISC 2009. Lecture Notes in Computer Science, vol 5805. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04355-0_26

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  • DOI: https://doi.org/10.1007/978-3-642-04355-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04354-3

  • Online ISBN: 978-3-642-04355-0

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