Looking for pairs that hard to separate: a quantum approach

Abstract

Determining the minimum number of states required by a deterministic finite automaton to separate a given pair of different words (to accept one word and to reject the other) is an important challenge. In this paper, we ask the same question for quantum finite automata (QFAs). We classify such pairs as easy and hard ones. We show that 2-state QFAs with real amplitudes can separate any easy pair with zero-error but cannot separate some hard pairs even in nondeterministic accepta