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Quantum and Stochastic Branching Programs of Bounded Width

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Automata, Languages and Programming (ICALP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2380))

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Abstract

We prove upper and lower bounds on the power of quantum and stochastic branching programs of bounded width. We show any NC1 language can be accepted exactly by a width-2 quantum branching program of polynomial length, in contrast to the classical case where width 5 is necessary unless NC1 = ACC. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in NC1.

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Author information

Authors and Affiliations

  1. Dept. of Theoretical Cybernetics, Kazan State University, 420008, Kazan, Russia

    Farid Ablayev

  2. Computer Science Department, University of New Mexico, Albuquerque, New Mexico, 87131

    Cristopher Moore

  3. Dept. of Math and Computer Science, San Jose State University, One Washington Square, San Jose, California, 95192

    Christopher Pollett

Authors
  1. Farid Ablayev
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  2. Cristopher Moore
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  3. Christopher Pollett
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Editor information

Editors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zentrum, ETH Zürich, 8092, Zürich, Switzerland

    Peter Widmayer  & Stephan Eidenbenz  & 

  2. Department of Languages and Sciences of the Computation E.T.S. de Ingeniería Informática, University of Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Francisco Triguero , Rafael Morales  & Ricardo Conejo ,  & 

  3. School of Cognitive and Computing Sciences, University of Sussex, Falmer, Brighton, BN1 9QN, UK

    Matthew Hennessy

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© 2002 Springer-Verlag Berlin Heidelberg

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Ablayev, F., Moore, C., Pollett, C. (2002). Quantum and Stochastic Branching Programs of Bounded Width. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_30

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  • DOI: https://doi.org/10.1007/3-540-45465-9_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43864-9

  • Online ISBN: 978-3-540-45465-6

  • eBook Packages: Springer Book Archive

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