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Basic Properties of Quantum Automata

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Abstract

This paper develops a theory of quantum automata and their slightly more general versions, q-automata. Quantum languages and η-quantum languages, 0≤η<1, are studied. Functions that can be realized as probability maps for q-automata are characterized. Quantum grammars are discussed and it is shown that quantum languages are precisely those languages that are induced by a quantum grammar. A quantum pumping lemma is employed to show that there are regular languages that are not η-quantum, 0≤η<1.

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  1. Department of Mathematics and Computer Science, University of Denver, Denver, Colorado, 80208

    Stanley Gudder

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  1. Stanley Gudder
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Gudder, S. Basic Properties of Quantum Automata. Foundations of Physics 30, 301–319 (2000). https://doi.org/10.1023/A:1003649201735

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