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International Workshop on Logic, Language, Information, and Computation

WoLLIC 2022: Logic, Language, Information, and Computation pp 88–104Cite as

Expressing Power of Elementary Quantum Recursion Schemes for Quantum Logarithmic-Time Computability

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13468))

Abstract

Quantum computing has been studied over the past four decades based on two computational models of quantum circuits and quantum Turing machines. To capture quantum polynomial-time computability, a new recursion-theoretic approach was taken lately by Yamakami [J. Symb. Logic 80, pp. 1546–1587, 2020] by way of schematic definitions, which constitute a few initial quantum functions and a few construction schemes, including composition, branching, and multi-qubit quantum recursion. By taking a similar step, we look into quantum logarithmic-time computability and further explore the expressing power of elementary schemes designed for such quantum computation. In particular, we introduce an elementary form of the quantum recursion, called the fast quantum recursion, which helps us capture quantum logarithmic-time computability.

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Notes

  1. 1.

    This notion should be distinguished from the same terminology used in [15].

  2. 2.

    We remark that Branch[g, h] can be expressed as an appropriate unitary matrix and thus it is a legitimate quantum operation to consider.

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Authors and Affiliations

  1. 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. Technische Universität Wien, Vienna, Austria

    Agata Ciabattoni

  2. University College London, London, UK

    Elaine Pimentel

  3. Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil

    Ruy J. G. B. de Queiroz

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Yamakami, T. (2022). Expressing Power of Elementary Quantum Recursion Schemes for Quantum Logarithmic-Time Computability. In: Ciabattoni, A., Pimentel, E., de Queiroz, R.J.G.B. (eds) Logic, Language, Information, and Computation. WoLLIC 2022. Lecture Notes in Computer Science, vol 13468. Springer, Cham. https://doi.org/10.1007/978-3-031-15298-6_6

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  • DOI: https://doi.org/10.1007/978-3-031-15298-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-15297-9

  • Online ISBN: 978-3-031-15298-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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