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Quantum noise can enhance algorithmic cooling

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.