  Heat-Bath Algorithmic Cooling techniques (HBAC) are techniques that are used
to purify a target element in a quantum system. These methods compress and
transfer entropy away from the target element into auxiliary elements of the
system. The performance of Algorithmic Cooling has been investigated under
ideal noiseless conditions. However, realistic implementations are imperfect
and for practical purposes, noise should be taken into account. Here we analyze
Heat-Bath Algorithmic Cooling techniques under realistic noise models.
Surprisingly, we find that noise can in some cases enhance the performance and
improve the cooling limit of Heat-Bath Algorithmic Cooling techniques. We
numerically simulate the noisy algorithmic cooling for the two optimal
strategies, the Partner Pairing, and the Two-sort algorithms. We find that for
both of them, in the presence of the generalized amplitude damping noise, the
process converges and the asymptotic purity can be higher than the noiseless
process. This opens up new avenues for increasing the purity beyond the
heat-bath algorithmic cooling.
