State Preservation of Open Quantum Systems

Abstract

Decoherence is a serious obstacle to the preservation of quantum superposition and entanglement over long periods of time (Giulini et al., 1996). Decoherence means non-unitary evolutions (Ai, Li, and Long, 2006;Niwa, Matsumoto, and Imai, 2002;Facchi et al., 2005) and results in the loss of information and/or probability leakage toward the environment. This issue has attracted much attention and a number of interesting schemes have been proposed to preserve coherence. Among these schemes are quantum error-. Error-avoiding codes encode information into the degenerate subspace of the error operators so that the information will not be affected by the error operators, while error-correcting codes restore the loss of information due to decoherence or quantum dissipation by monitoring the system and conditionally carrying on suitable feedback control. Their applications are limited by the requirement of using redundant qubit resources. Bang-bang control uses high-frequency pulses to average out the decoherence effect. However, it has the essential requirement that the bath retains some memory of its interaction with the system, so it is not useful for a system subject to Markovian decoherence. Lidar and Schneider (2005) therefore proposed a new method called tracking-control to solve the problem of stabilizing the coherence of a single qubit subject to Markovian decoherence. Recently, Zhang et al. (2010) proposed a feedback control strategy based on quantum weak measurements to protect the coherence of a qubit system in which the stochastic noise was considered. However, their work was restricted to a single-qubit system and they only Control of Quantum Systems: Theory and Methods, First Edition. Shuang Cong.