Improved constructions of quantum automata

We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use [email protected] 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.

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