  This MS thesis explores the effects and origins of a 'noise with memory' in
the dynamics of an open quantum system. The system considered here is a
multi-qubit register performing the Grover's quantum search algorithm. We show
that a Markovian-correlated noise can enhance the efficiency of the algorithm
over a time correlation-less noise. We also analytically find the set of
necessary and sufficient conditions for the algorithm's success probability to
remain invariant with respect to the number of noisy sites in the register and
point out that these conditions hold irrespective of the presence of
time-correlations in the noise. We then investigate the origins of the type of
noise considered. In this regard, a 'collisional model' is constructed that
exactly reproduces the noisy evolution of the open system. Non-Markovianity in
the system's evolution is then assessed using two well-known measures and they
are shown to be non-coincident. Our model is then slightly modified to
accommodate an elementary thermal bath. There we show that increasing the
bath's temperature increases information drainage from the system.
