Novel Technique for Robust Optimal Algorithmic Cooling

Abstract

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.

Exponential improvement for quantum cooling through finite-memory effects

“…We first show that in the asymptotic limit of repeated cycles, the memory depth of the protocol plays an important role and can lead to exponential improvement over the Markovian case; in fact, perhaps surprisingly, the role of memory depth is more significant than that of the ability of the agent to implement multi-partite interactions between the system and machines at each step. Our result coincides with the asymptotic limit of heat-bath algorithmic cooling protocols [36][37][38][39][40][41][42][43] and provides a wide-ranging generalization of this setting that permits adaptive strategies and is applicable for all system and finite dimensional environment structures. We further show that adaptive strategies can out-perform non-adaptive ones and provide a finite time cooling advantage.…”

No-go Theorem of Purification

“…quantum gates can be applied perfectly. Similar setting has been investigated in the heat-bath algorithmic cooling where purification is translated to cooling and it aims at compressing and transferring the entropy of the target element to the auxiliary one [12][13][14][15]. But this is a key caveat, namely the assumption that purification operations can be applied perfectly [21].…”

Breaking the limits of purification: Postselection enhances heat-bath algorithmic cooling

“…1a-b), entropy can be shuttled to the bath to cool the multi-qubit system [1][2][3]. This idea has been comprehensively investigated [4][5][6][7][8][9][10][11][12] and experimentally demonstrated [13,14].…”

“…It was superseded by the technique of Ref. [8], which allows the ultimate cooling limit to be achieved without any knowledge of the state being cooled; we sketch this technique here (see Fig. 1 a-b)).…”

“…where 𝜎 𝑥 is a Pauli matrix and all of the off-diagonal entries are null, acts on the state to shift the larger probabilities like e 𝜀 toward the |g part of the system and the smaller probabilities like e −𝜀 toward the opposite end. This "two-sort" unitary can be efficiently implemented [8]. The entire process is then repeated until, with a high degree of probability, the state reaches the theoretically coldest (most pure) state possible.…”