Abstract
Quantum state machines are introduced.Amplitudes of computational paths, computational bases,superposition states, and evolution operators arediscussed. The main part of the paper develops a theoryof quantum automata and their slightly moregeneral versions, q-automata. Quantum languages andη-quantum languages, 0 ≤ η < 1, arestudied. A method is given for reducing the size of thestate space. Functions that can be realized as probabilitymaps for q-automata are characterized. Quantum gates arediscussed. A quantum pumping lemma is employed to showthat there are regular languages that are not η-quantum, 0 ≤ η < 1. The papercloses with a list of open problems.
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Gudder, S. Quantum Automata: An Overview. International Journal of Theoretical Physics 38, 2261–2282 (1999). https://doi.org/10.1023/A:1026663432352
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DOI: https://doi.org/10.1023/A:1026663432352