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Complexity Bounds of Constant-Space Quantum Computation

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Developments in Language Theory (DLT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9168))

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Abstract

We model constant-space quantum computation as measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing their behaviors and explore their properties. In particular, when the automata halt “in finite steps,” they must terminate in worst-case liner time. Even if all computation paths of bounded-error automata do not terminate, it suffices to focus only on computation paths that terminate after exponentially many steps. We present a classical simulation of those automata on multi-head probabilistic finite automata with cut points. Moreover, we discuss how the power of the automata varies as the automata’s acceptance criteria change to error free, one-sided error, bounded error, and unbounded error.

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Authors and Affiliations

  1. Department of Information Science, University of Fukui, 3-9-1 Bunkyo, Fukui, 910-8507, Japan

    Tomoyuki Yamakami

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  1. Tomoyuki Yamakami
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Correspondence to Tomoyuki Yamakami .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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Yamakami, T. (2015). Complexity Bounds of Constant-Space Quantum Computation. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_34

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  • DOI: https://doi.org/10.1007/978-3-319-21500-6_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

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