The Complexity of Probabilistic versus Quantum Finite Automata

Details The Complexity of Probabilistic versus Quantum Finite Automata The Complexity of Probabilistic versus Quantum Finite Automata

2003-09-09

arxiv.org/abs/quant-ph/0309080v1

SOFSEM 2002 Proceedings,, pp. 273-278

Physics

Quantum Physics

6 pages, 2 figures

Scientific paper

We present a language $L_n$ which is recognizable by a probabilistic finite
automaton (PFA) with probability $1 - \epsilon$ for all $\epsilon > 0$ with
$O(log^2n)$ states, with a deterministic finite automaton (DFA) with O(n)
states, but a quantum finite automaton (QFA) needs at least $2^{\Omega(n/ \log
n)}$ states.

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