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Optimal Control Strategy for Coherence-preserving Based on Two-level Open Quantum Systems

Zonghai Chen

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The coherence-preserving of two-level open quantum systems is recognized as a key to preserve the striking feature of the parallel character of the quantum information processing,which is crucial for implementing the quantum theory into reality. Aiming at the problem,in order to reduce this unexpected decoherence effect,the quantum master equation was mainly investigated. The orthogonal basis of geometric algebra was used to convert the quantum master equation into the state-space model; in which the useful coherent vector was attained. Then the corresponding recursive optimal control algorithm was designed to achieve both the maximal suppression of decoherence and the control energy minimizing based on a typical two-level quantum system. Afterwards,some tips of how to choose the parameters were discussed. Simulation results verify its effectiveness and superiority to coherence-preserving.

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The coherence-preserving of two-level open quantum systems is recognized as a key to preserve the striking feature of the parallel character of the quantum information processing,which is crucial for implementing the quantum theory into reality. Aiming at the problem,in order to reduce this unexpected decoherence effect,the quantum master equation was mainly investigated. The orthogonal basis of geometric algebra was used to convert the quantum master equation into the state-space model; in which the useful coherent vector was attained. Then the corresponding recursive optimal control algorithm was designed to achieve both the maximal suppression of decoherence and the control energy minimizing based on a typical two-level quantum system. Afterwards,some tips of how to choose the parameters were discussed. Simulation results verify its effectiveness and superiority to coherence-preserving.
This paper addresses the optimal control of quantum coherence in multi-level systems, modeled by the Lindblad master equation, which captures both unitary evolution and environmental dissipation. We develop an energy minimization framework to control the evolution of a qutrit (three-level) quantum system while preserving coherence between states. The control problem is formulated using Pontryagin's Minimum Principle in the form of Gamkrelidze, incorporating state constraints to ensure coherence remains within desired bounds. Our approach accounts for Markovian decoherence, demonstrating that the Lindblad operator is non-unital, which reflects the irreversible decay processes inherent in the system. The results provide insights into effectively maintaining quantum coherence in the presence of dissipation.
This paper addresses the optimal control of quantum coherence in multi-level systems, modeled by the Lindblad master equation, which captures both unitary evolution and environmental dissipation. We develop an energy minimization framework to control the evolution of a qutrit (three-level) quantum system while preserving coherence between states. The control problem is formulated using Pontryagin’s Minimum Principle in the form of Gamkrelidze, incorporating state constraints to ensure coherence remains within desired bounds. Our approach accounts for Markovian decoherence, demonstrating that the Lindblad operator is non-unital, which reflects the irreversible decay processes inherent in the system. The results provide insights into effectively maintaining quantum coherence in the presence of dissipation.
The decoherence suppression issue is studied for two-level quantum systems based on coherent control strategy.The model of two-level open quantum systems under coherent control is formulated,in which the decoherence suppression is equivalent to the decoupling problem of the system from environmental noises.Then,an open-loop control is designed to suppress decoherence,which is shown to be capable of asymptotically decoupling a part of the dynamic variables of the system from the environmental noises.Finally,feedback control strategy is introduced so that the corresponding state variables can be precisely decoupled form the environmental noises without being affected by the noises induced by quantum measurement in feedback control.
The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge of preserving relevant nonclassical features at the level of device operation. A major obstacle is decoherence, which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. Here we review recent advances in optimal control methodology that allow typical tasks in device operation for open quantum systems to be tackled and discuss examples of relaxation-optimized dynamics. Optimal control theory is also a useful tool to exploit the environment for control. We discuss examples and point out possible future extensions.
The interpretation to the mechanism of interaction of light and matter is used in new quantum devices designing for the optical information storage.For reducing the unexpected decoherence effect in a Λ-typed three-level atom system,the master equation of an atomic system is investigated to find a set of states that have zero spontaneous decay rates.Two laser fields are introduced to prepare the decoherence-free state by using decoherence-free subspace(DFS) strategy to suppress spontaneous emission for the decoupling of the system's state and the environment.Theoretical analysis verifys its effectiveness to coherence-preserving.