Achievable Polarization for Heat-Bath Algorithmic Cooling

Abstract

Highly pure quantum states play a central role in applications of quantum information science, both as initial states for quantum algorithms and as resources for quantum error correction. Controlled preparation of pure enough quantum states that satisfy the threshold for quantum error correction remains a challenge, not only for ensemble implementations like nuclear magnetic resonance (NMR) or electron spin resonance (ESR) but also for other technologies. Heat-bath algorithmic cooling (HBAC) is a promising method to increase the purity of a set of qubits coupled to a bath. In this thesis, we investigated the achievable polarization of this technique by analyzing the limit when no more entropy can be extracted from the system. In particular, we give an analytic form of the maximum polarization achievable for the case when the initial state is totally mixed, and the corresponding steady state of the whole system. Furthermore, we give the number of steps needed to get a specific required polarization (the exact number for the two qubit case and an upper bound for more general cases).