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Mirrors and Memory in Quantum Automata

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Quantitative Evaluation of Systems (QEST 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13479))

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Abstract

In this paper we start from the simplest form of Quantum Finite Automata (QFAs), namely Measure-Once QFAs with cut-point. First we elaborate on a variant of their semantics that can be obtained through a shift from the Schrödinger to the Heisenberg picture of Quantum Mechanics. In the Schrödinger picture states evolve in time while observables remain constant, while in the Heisenberg one states are constant and observables evolve. Interestingly, in the case of a QFA such shift reverts time-evolution. However, the equivalence of the two pictures over the class of QFAs holds thanks to the closure of the class with respect to language mirroring. Since the expressive power of such class of automata remains limited to infinite languages, we then consider their extension with bounded (multi-letter QFAs) and unbounded memory. Unfortunately, while bounded memory enhances the expressive power, the unbounded memory approach does not behave as one would expect.

This work is partially supported by PRIN MUR project Noninterference and Reversibility Analysis in Private Blockchains (NiRvAna) - 20202FCJM and by GNCS INdAM project LESLIE.

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Notes

  1. 1.

    Some work has been done for Quantum Cellular Automata, where the equivalence between Schrödinger model and Heisenberg model has been proved (e.g., [4]).

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Authors and Affiliations

  1. Department of Mathematics, Computer Science and Physics, University of Udine, Udine, Italy

    Carla Piazza & Riccardo Romanello

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  1. Carla Piazza
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  2. Riccardo Romanello
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Correspondence to Riccardo Romanello .

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Editors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Erika Ábrahám

  2. University of Southern California, Los Angeles, CA, USA

    Marco Paolieri

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Piazza, C., Romanello, R. (2022). Mirrors and Memory in Quantum Automata. In: Ábrahám, E., Paolieri, M. (eds) Quantitative Evaluation of Systems. QEST 2022. Lecture Notes in Computer Science, vol 13479. Springer, Cham. https://doi.org/10.1007/978-3-031-16336-4_18

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  • DOI: https://doi.org/10.1007/978-3-031-16336-4_18

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