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STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
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STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Dense quantum coding and a lower bound for 1-way quantum automata
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the Lower Bounds for One-Way Quantum Automata
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FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
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The main purpose of this paper is to show that we can exploit the difference in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It is shown that, for each n, 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 驴(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.