  Continuous-time quantum walks may be exploited to enhance spatial search,
i.e., for finding a marked element in a database structured as a complex
network. However, in practical implementations, the environmental noise has
detrimental effects, and a question arises on whether noise engineering may be
helpful in mitigating those effects on the performance of the quantum
algorithm. Here we study whether time-correlated noise inducing
non-Markovianity may represent a resource for quantum search. In particular, we
consider quantum search on a star graph, which has been proven to be optimal in
the noiseless case, and analyze the effects of independent random telegraph
noise (RTN) disturbing each link of the graph. Upon exploiting an exact code
for the noisy dynamics, we evaluate the quantum non-Markovianity of the
evolution, and show that it cannot be considered as a resource for this
algorithm, since its presence is correlated with lower probabilities of success
of the search.
