  Continuous-time quantum walks have proven to be an extremely useful framework
for the design of several quantum algorithms. Often, the running time of
quantum algorithms in this framework is characterized by the quantum hitting
time: the time required by the quantum walk to find a vertex of interest with a
high probability. In this article, we provide improved upper bounds for the
quantum hitting time that can be applied to several CTQW-based quantum
algorithms. In particular, we apply our techniques to the glued-trees problem,
improving their hitting time upper bound by a polynomial factor: from $O(n^5)$
to $O(n^2\log n)$. Furthermore, our methods also help to exponentially improve
the dependence on precision of the continuous-time quantum walk based algorithm
to find a marked node on any ergodic, reversible Markov chain by Chakraborty et
al. [PRA 102, 022227 (2020)].
