An algorithm given by Ambainis and Freivalds [1] constructs a quantum finite automaton (QFA) with O(log p) states recognizing the language Lp = {ai| i is divisible by p} with probability 1 − ε, for any ε > 0 and arbitrary prime p. In [4] we gave examples showing that the algorithm is applicable also to quantum automata of very limited size. However, the Ambainis-Freivalds algoritm is tailored to constructing a measure-many QFA (defined by Kondacs andWatrous [2]), which cannot be implemented on existing quantum computers. In this paper we modify the algorithm to construct a measure-once QFA of Moore and Crutchfield [3] and give examples of parameters for this automaton. We show for the language Lp that a measure-once QFA can be twice as space efficient as measure-many QFA’s.
CITATION STYLE
Bērziņa, A., & Bonner, R. (2001). Ambainis-Freivalds’ algorithm for measure-once automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2138, pp. 83–93). Springer Verlag. https://doi.org/10.1007/3-540-44669-9_10
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