  Heat-bath algorithmic cooling (HBAC) provides algorithmic ways to improve the
purity of quantum states. These techniques are complex iterative processes that
change from each iteration to the next and this poses a significant challenge
to implementing these algorithms. Here, we introduce a new technique that on a
fundamental level, shows that it is possible to do algorithmic cooling and even
reach the cooling limit without any knowledge of the state and using only a
single fixed operation, and on a practical level, presents a more feasible and
robust alternative for implementing HBAC. We also show that our new technique
converges to the asymptotic state of HBAC and that the cooling algorithm can be
efficiently implemented; however, the saturation could require exponentially
many iterations and remains impractical. This brings HBAC to the realm of
feasibility and makes it a viable option for realistic application in quantum
technologies.
