Basic Properties of Quantum Automata

Foundations of Physics 30 (2):301-319 (2000)

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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DOI 10.1023/A:1003649201735
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