  Reachability analysis plays a central role in system design and verification.
The reachability problem, denoted $\Diamond^J\,\Phi$, asks whether the system
will meet the property $\Phi$ after some time in a given time interval $J$.
Recently, it has been considered on a novel kind of real-time systems --
quantum continuous-time Markov chains (QCTMCs), and embedded into the
model-checking algorithm. In this paper, we further study the repeated
reachability problem in QCTMCs, denoted $\Box^I\,\Diamond^J\,\Phi$, which
concerns whether the system starting from each \emph{absolute} time in $I$ will
meet the property $\Phi$ after some coming \emph{relative} time in $J$. First
of all, we reduce it to the real root isolation of a class of real-valued
functions (exponential polynomials), whose solvability is conditional to
Schanuel's conjecture being true. To speed up the procedure, we employ the
strategy of sampling. The original problem is shown to be equivalent to the
existence of a finite collection of satisfying samples. We then present a
sample-driven procedure, which can effectively refine the sample space after
each time of sampling, no matter whether the sample itself is successful or
conflicting. The improvement on efficiency is validated by randomly generated
instances. Hence the proposed method would be promising to attack the repeated
reachability problems together with checking other $\omega$-regular properties
in a wide scope of real-time systems.
