2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160795We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use \frac{4}ε \log 2p + O(1) states to recognize a language that requires p states classically. The construction is both substantially simpler and achieves a better constant in the front of \log p than the previously known construction of Ambainis and Freivalds (quant-ph/9802062). Similarly to Ambainis and Freivalds, our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some results in this direction.9 pagesQuantum Physicstext