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Algebraic Results on Quantum Automata

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Abstract

We use tools from the algebraic theory of automata to investigate the class of languages recognized by two models of Quantum Finite Automata (QFA): Brodsky and Pippenger's end-decisive model (which we call BPQFA) and a new QFA model (which we call LQFA) whose definition is motivated by implementations of quantum computers using nucleo-magnetic resonance (NMR). In particular, we are interested in LQFA since NMR was used to construct the most powerful physical quantum machine to date. We give a complete characterization of the languages recognized by LQFA and by Boolean combinations of BPQFA. It is a surprising consequence of our results that LQFA and Boolean combinations of BPQFA are equivalent in language recognition power.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization and Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 2T2, Canada

    Andris Ambainis & Arnolds Kikusts

  2. Departement d'Informatique 2500, Boul. Universite, Sherbrooke, Quebec, J1K 2R1, Canada

    Martin Beaudry

  3. Computer Science Division, University of California, Berkeley, CA 94720, USA

    Marats Golovkins

  4. School of Computer Science, McGill University, 3480 rue University, Montreal, Quebec, H3A 2A7, Canada

    Mark Mercer & Denis Therien

Authors
  1. Andris Ambainis
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  2. Martin Beaudry
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  3. Marats Golovkins
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  4. Arnolds Kikusts
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  5. Mark Mercer
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  6. Denis Therien
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Corresponding authors

Correspondence to Andris Ambainis, Martin Beaudry, Marats Golovkins, Arnolds Kikusts, Mark Mercer or Denis Therien.

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Ambainis, A., Beaudry, M., Golovkins, M. et al. Algebraic Results on Quantum Automata. Theory Comput Syst 39, 165–188 (2006). https://doi.org/10.1007/s00224-005-1263-x

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  • DOI: https://doi.org/10.1007/s00224-005-1263-x

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