Exploiting the Difference in Probability Calculation between Quantum and Probabilistic Computations

Masami AMANO  Kazuo IWAMA  Raymond H. PUTRA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.5   pp.1004-1011
Publication Date: 2004/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
quantum finite automata,  quantum computing,  finite automata,  

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The main purpose of this paper is to show that we can exploit the difference (l1-norm and l2-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It is shown that there is a finite language L which contains sentences of length up to O(nc+1) such that: (i) There is a one-way quantum finite automaton (qfa) of O(nc+4) states which recognizes L. (ii) However, if we try to simulate this qfa by a probabilistic finite automaton (pfa) using the same algorithm, then it needs Ω(n2c+4) states. It should be noted that we do not prove real lower bounds for pfa's but show that if pfa's and qfa's use exactly the same algorithm, then qfa's need much less states.