1-way quantum finite automata: strengths, weaknesses and generalizations

  • Authors:

  • Andris Ambainis;Rusins Freivalds

  • Affiliations:

  • -;-

  • Venue:
  • FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
  • Year:
  • 1998

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Abstract

We study 1-way quantum finite automata (QFAs).First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFAs can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata.Second, we show that 1-way QFAs can be very space-efficient. We construct a 1-way QFA that is exponentially smaller than any equivalent classical (even randomized) finite automaton. We think that this construction may be useful for design of other space-efficient quantum algorithms.Third, we consider several generalizations of 1-way QFAs. Here, our goal is to find a model which is more powerful than 1-way QFAs keeping the quantum part as simple as possible.