Two-way finite automata with quantum and classical states

  • Authors:

  • Andris Ambainis;John Watrous

  • Affiliations:

  • Computer Science Division, University of California, Berkeley, CA;Department of Computer Sciences, University of Calgary, Calgary, Alberta, Canada T2N 1N4

  • Venue:
  • Theoretical Computer Science - Natural computing
  • Year:
  • 2002

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Abstract

We introduce 2-way finite automata with quantum and classical states (2qcfa's). This is a variant on the 2-way quantum finite automata (2qfa) model which may be simpler to implement than unrestricted 2qfa's; the internal state of a 2qcfa may include a quantum part that may be in a (mixed) quantum state, but the tape head position is required to be classical.We show two languages for which 2qcfa's are better than classical 2-way automata. First, 2qcfa's can recognize palindromes, a language that cannot be recognized by 2-way deterministic or probabilistic finite automata. Second, in polynomial time 2qcfa's can recognize {anbn|n ∈ N}, a language that can be recognized classically by a 2-way probabilistic automaton but only in exponential time.