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Control Theory and Technology

Feedback stabilization of N-dimensional stochastic quantum systems based on bang-bang control

Xiaqing Sun, Sen Kuang, Yanan Liu, Juan Zhou, Shuang Cong

Published Aug 1, 2017• 1 citation
Publisher
DOI
10.1007/s11768-017-7061-6

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This letter considers target state preparation for Markovian open quantum systems subject to continuous measurement. Conditions on invariant and attractive subspaces are investigated, which ensure the stabilization of the target state/subspace. For a class of open quantum systems with time delay in the feedback loop, a bang-bang-like control law is proposed, and the stability of the feedback control strategy is proved. An example of four-level Markovian open quantum systems is presented to demonstrate the effectiveness of the proposed control strategy.
The laws of thermodynamics are a cornerstone for describing nanoscale and open quantum systems. However, formulating these laws for systems under continuous feedback control and under experimentally relevant conditions is challenging. In this work, we lay out a formalism for the laws of thermodynamics in an open quantum system under continuous measurement and feedback described by a Quantum Fokker Planck Master Equation. We derive expressions for work, heat, and measurement-induced energy changes, and we investigate entropy production and fluctuation theorems. We illustrate our results with a continuous version of a measurement-driven Szilard engine, as well as a work extraction scheme in a two-level system under bang-bang control. Our results provide insights into the energetics as well as the irreversibility of classical and quantum systems under continuous feedback control.