Improved constructions of quantum automata

Authors:
Andris Ambainis;Nikolajs Nahimovs
Affiliations:
University of Latvia, Department of Computer Science, Raina bulv. 19, Riga, LV-1586, Latvia;University of Latvia, Department of Computer Science, Raina bulv. 19, Riga, LV-1586, Latvia
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use 4@elog2p states to recognize a language that requires p states classically. The construction is both substantially simpler and achieves a better constant in the front of logp than the previously known construction. Our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some results in this direction.