Publié le 24 août 2020 | Mis à jour le 24 août 2020

Simone Martini: Quantum Turing Machines

Computations and Measurements

Guerrini, S.; Martini, S.; Masini, A. Quantum Turing Machines: Computations and Measurements. Appl. Sci. 2020, 10, 5551.

Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not been fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example being the intrinsic infinite nature of any quantum computation. In this paper, we propose a definition of QTM, which extends and unifies the notions of Deutsch and Bernstein & Vazirani. In particular, we allow both arbitrary quantum input, and meaningful superpositions of computations, where some of them are “terminated” with an “output”, while others are not. For some infinite computations an “output” is obtained as a limit of finite portions of the computation. We propose a natural and robust observation protocol for our QTMs, which does not modify the probability of the possible outcomes of the machines. Finally, we use QTMs to define a class of quantum computable functions—any such function is a mapping from a general quantum state to a probability distribution of natural numbers. We expect that our class of functions, when restricted to classical input-output, will not be different from the set of the recursive functions.

  • Auteur(s)
    Simone Martini - Fellow du Collegium de Lyon 2018-2019
    Dipartimento di Informatica—Scienza e Ingegneria, Università di Bologna, 40126 Bologna, Italy
    Inria Sophia-Antipolis, 06902 Valbonne, France
    Research partially conducted while on sabbatical leave at the Collegium—Lyon Institute for Advanced Studies, 2018–2019.

    Stefano Guerrini
    LIPN, UMR 7030 CNRS, Institut Galilée, Université Sorbonne Paris Nord, 93430 Villetaneuse, France

    Andrea Masini

    Dipartimento di Informatica, Università di Verona, 37134 Verona, Italy