Efficient probability amplification in two-way quantum finite automata

In classical computation, one only needs to sequence O([email protected]) identical copies of a given probabilistic automaton with one-sided error p 0}, Kondacs and Watrous use a different probability amplification method, which yields machines with O(([email protected])^2) states, and with runtime O([email protected]|w|), where w is the input string. In this paper, we examine significantly more efficient techniques of probability amplification. One of our methods produces machines which decide L in O(|w|) time (i.e. the running time does not depend on the error bound) and which have O(([email protected])^2^c) states for any given constant c>1. Other methods, yielding machines whose state complexities are polylogarithmic in [email protected], including one which halts in o(log([email protected])|w|) time, are also presented.