Novel Technique for Robust Optimal Algorithmic Cooling

Heat-bath algorithmic cooling 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 heat-bath algorithmic cooling. We also show that our new technique converges to the asymptotic state of heat-bath algorithmic cooling and that the cooling algorithm can be efficiently implemented; however, the saturation could require exponentially many iterations and remains impractical. This brings heat-bath algorithmic cooling to the realm of feasibility and makes it a viable option for realistic application in quantum technologies.

Figure 1

The pictorial description of an iteration. The input is the list of the diagonal elements of the full density matrix, $\{{\lambda }^t\}$. The reset step first merges every two neighboring elements (partial trace) and then replaces the reset qubit with ${\rho }_R$ which splits each element into two elements again. Next, the $U_{\mathrm{TS}}$ swaps all the neighboring elements except for the first and the last one.

Figure 2

This plot shows that the maximum of the NBDS for implementations of PPA grows exponentially with the number of computation qubits $n$. The $y$ axis is a logarithmic scale. Different plots correspond to different reset polarizations $\epsilon$.

Figure 3

This plot shows the polarization of the first qubit vs iterations. This is for the simulation of PPA for two computation qubits and one reset qubit, with different amounts of the state estimation errors $\sigma$.