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

被引:157
作者
Ambainis, A [1 ]
Freivalds, R [1 ]
机构
[1] Univ Calif Berkeley, Div Comp Sci, Berkeley, CA 94720 USA
来源
39TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS | 1998年
关键词
D O I
10.1109/SFCS.1998.743469
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
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.
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页码:332 / 341
页数:2
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