  We study numerically the population transfer protocol on the Quantum Random
Energy Model and its relation to quantum computing, for system sizes of $n\leq
20$ quantum spins. We focus on the energy matching problem, i.e. finding
multiple approximate solutions to a combinatorial optimization problem when a
known approximate solution is provided as part of the input. We study the
delocalization process induced by the population transfer protocol by observing
the saturation of the Shannon entropy of the time-evolved wavefunction as a
measure of its spread over the system. The scaling of the value of this entropy
at saturation with the volume of the system identifies the three known
dynamical phases of the model. In the non-ergodic extended phase, we observe
that the time necessary for the population transfer to complete follows a
long-tailed distribution. We devise two statistics to quantify how effectively
and uniformly the protocol populates the target energy shell. We find that
population transfer is most effective if the transverse-field parameter
$\Gamma$ is chosen close to the critical point of the Anderson transition of
the model. In order to assess the use of population transfer as a quantum
algorithm we perform a comparison with random search. We detect a "black box"
advantage in favour of PT, but when the running times of population transfer
and random search are taken into consideration we do not see strong indications
of a speedup at the system sizes that are accessible to our numerical methods.
We discuss these results and the impact of population transfer on NISQ devices.
