  This paper studies three kinds of long-term behaviours, namely reachability,
repeated reachability and persistence, of quantum Markov chains (qMCs). As a
stepping-stone, we introduce the notion of bottom strongly connected component
(BSCC) of a qMC and develop an algorithm for finding BSCC decompositions of the
state space of a qMC. As the major contribution, several (classical) algorithms
for computing the reachability, repeated reachability and persistence
probabilities of a qMC are presented, and their complexities are analysed.
