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Journal of Physics A Mathematical and General

Maximal suppression of decoherence in Markovian quantum systems

Jing Zhang, Chunwen Li, Re-Bing Wu, Tzyh‐Jong Tarn, Xiao-Shu Liu

Published Jul 6, 2005• 42 citations
Publisher

Abstract

In this paper, we design an optimal control law to suppress decoherence effects in Markovian open quantum systems. The optimal control law is subject to the tracking precision of the trajectory governed by the free system, which is ideally free from decoherence. We observe from numerical simulation that the undesired decohering dynamics can be partially squeezed out in most systems. Moreover, we observe the existence of sinusoidally oscillating resonant modes that play dominant roles in the controlled trajectory, which can be easily realized by continuous wave pulses. These key features are strictly demonstrated in subsequent analysis under proper assumptions. For systems in which the coherent control does not work, we suggest a feedback control strategy to extend the applicability of control to wider class of systems.

DOI
10.1088/0305-4470/38/29/013

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In this paper, we design an optimal control law to suppress decoherence effects in Markovian open quantum systems. The optimal control law is subject to the tracking precision of the trajectory governed by the free system, which is ideally free from decoherence. We observe from numerical simulation that the undesired decohering dynamics can be partially squeezed out in most systems. Moreover, we observe the existence of sinusoidally oscillating resonant modes that play dominant roles in the controlled trajectory, which can be easily realized by continuous wave pulses. These key features are strictly demonstrated in subsequent analysis under proper assumptions. For systems in which the coherent control does not work, we suggest a feedback control strategy to extend the applicability of control to wider class of systems.
The problem of optimal control of non-Markovian open quantum system via weak measurement is presented. Based on the non-Markovian master equation, we evaluate exactly the non-Markovian effect on the dynamics of the system of interest interacting with a dissipative reservoir. We find that the non-Markovian reservoir has dual effects on the system: dissipation and backaction. The dissipation exhausts the coherence of the quantum system, whereas the backaction revives it. Moreover, we design the control Hamiltonian with the control laws attained by the stochastic optimal control and the corresponding optimal principle. At last, we considered the exact decoherence dynamics of a qubit in a dissipative reservoir composed of harmonic oscillators, and demonstrated the effectiveness of our optimal control strategy. Simulation results showed that the coherence will completely lost in the absence of control neither in non-Markovian nor Markovian system. However, the optimal feedback control steers it to a stationary stochastic process which fluctuates around the target. In this case the decoherence can be controlled effectively, which indicates that the engineered artificial reservoirs with optimal feedback control may be designed to protect the quantum coherence in quantum information and quantum computation.
We study the optimal control problem in a non-Markovian open quantum system. The quantum system of interest is coupled to its local environment, which is dissipative in nature and tends to decay the quantum system. Based on the non-Markovian master equation, we study the non-Markovian effects on the system dynamics. The non-Markovian environment has dual effects on the quantum system: the dissipation and the backaction. The dissipation effect makes the system lose of quantum features, whereas the backaction revives it. We further design quantum control laws to control the system. The optimal control principle is studied to steer to quantum state to a target state. Finally, as an example, we used the optimal control method to control the quantum decoherence.
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 ability to optimally control quantum systems in the presence of environmentally-induced decoherence is important for many physical and chemical problems.We discuss both theoretical and experimental aspects of optimal control of open quantum systems. The theoretical analysis is based on fundamental concepts of open-system controllability and control landscapes. These theoretical advances lay the groundwork for practical applications, including numerical simulations and experimental implementations of adaptive feedback control. In particular, the adaptive approach was utilized to implement coherent control of decoherence, which uses coherent (unitary) preparation and manipulation of an open quantum system to significantly alter its incoherent (non-unitary) dynamics caused by coupling to an environment. We also discuss other applications, including optimal dynamic discrimination of similar quantum systems and optimal control of high-fidelity quantum gates in the presence of decoherence.
We investigate the optimal control problem in non-Markovian open, dissipative quantum system. Optimal control using Pontryagin maximum principle of this problem has been specifically derived. The influences of Ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions w0Lt wc, w0ap wcor w0Gt wcrespectively. The optimal control process shows its remarkable influences to the decoherence dynamics. The temperature is a key factor in the decoherence dynamics. We analysis the optimal decoherence control in high temperature, intermediate temperature, and low temperature reservoirs respectively. It implies that designing some engineered reservoirs with the controlled coupling and state of the environment can slow down the decoherence rate and delay the decoherence time. Moreover, we compared the non-Markovian optimal decoherence control with the Markovian one, we find that with non-Markovian the engineered artificial reservoirs are better than with the Markovian approximate in controlling the open, dissipative quantum systempsilas decoherence.
To make full use of the amazing characteristics of quantum states, control of open quantum systems is of great significance in practical applications. This paper studies a more practical control problem where the decoherence parameter is not known exactly. The problem is considered in two phases. First, the unknown decoherence strength is estimated based on continuous measurements and an appropriately designed control. Then, Markovian feedback control is designed to deal with the decoherence effect based on the accurate parameter estimation. It is shown that state transfer with a high probability can be achieved by designing the feedback gains and the measurement. Moreover, good state transfer performance can be guaranteed even there exists an estimation error on the decoherence strength. Simulation studies are included to demonstrate the effectiveness of the proposed approach.