We study the reachability problem of a quantum system modelled by a quantum
automaton. The reachable sets are chosen to be boolean combinations of (closed)
subspaces of the state space of the quantum system. Four different reachability
properties are considered: eventually reachable, globally reachable, ultimately
forever reachable, and infinitely often reachable. The main result of this
paper is that all of the four reachability properties are undecidable in
general; however, the last three become decidable if the reachable sets are
boolean combinations without negation
