1way quantum finite automata: strengths, weaknesses and generalizations
Abstract
We study 1way 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 (over 0.98), then the power of 1way QFAs is equal to the power of 1way reversible automata. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata. Second, we show that 1way QFAs can be very spaceefficient. Namely, we construct a 1way QFA which is exponentially smaller than any equivalent classical (even randomized) finite automaton. This construction may be useful for design of other spaceefficient quantum algorithms. Third, we consider several generalizations of 1way QFAs. Here, our goal is to find a model which is more powerful than 1way QFAs keeping the quantum part as simple as possible.
 Publication:

arXiv eprints
 Pub Date:
 February 1998
 DOI:
 10.48550/arXiv.quantph/9802062
 arXiv:
 arXiv:quantph/9802062
 Bibcode:
 1998quant.ph..2062A
 Keywords:

 Quantum Physics;
 Computational Complexity
 EPrint:
 23 pages LaTeX, 1 figure, to appear at FOCS'98