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IET Control Theory and Applications

Sampled‐data design for robust control of open two‐level quantum systems with operator errors

Daoyi Dong, Ian R. Petersen, Yuanlong Wang, X. X. Yi, HERSCHEL A. RABITZ

Published Aug 24, 2016• 12 citations
Publisher

Abstract

This study proposes a sampled‐data design method for robust control of open two‐level quantum systems with operator errors. The required control performance is characterised using the concept of a sliding mode domain related to fidelity, coherence or purity. The authors have designed a control law offline and then utilise it online for a two‐level system subject to decoherence with operator errors in the system model. They analyse three cases of approximate amplitude damping decoherence, approximate phase damping decoherence and approximate depolarising decoherence. They design specific sampling periods for these cases that can guarantee the required control performance.

DOI
10.1049/iet-cta.2016.0368

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This study proposes a sampled‐data design method for robust control of open two‐level quantum systems with operator errors. The required control performance is characterised using the concept of a sliding mode domain related to fidelity, coherence or purity. The authors have designed a control law offline and then utilise it online for a two‐level system subject to decoherence with operator errors in the system model. They analyse three cases of approximate amplitude damping decoherence, approximate phase damping decoherence and approximate depolarising decoherence. They design specific sampling periods for these cases that can guarantee the required control performance.
This paper presents a sampled-data design approach for decoherence control of a single qubit with operator errors. The required control performance is defined using a sliding mode domain and the control law is designed offline and then utilized online with a single qubit subject to decoherence with operator errors. Three cases are analyzed in detail including approximate amplitude damping decoherence, approximate phase damping decoherence and approximate depolarizing decoherence. Sampling periods are specifically designed for these cases to guarantee the required control performance.
Due to the influence of decoherence, the quantum state probably evolves from the initial pure state to the mixed state, resulting in loss of fidelity, coherence and purity, which is deteriorating for quantum information transmission. Thus, in quantum engineering, quantum control should not only realize the transfer and track of quantum states through manipulation of the external electromagnetic field but also enhance the robustness against decoherence. In this paper, we aim to design a control law to steer the system into the sliding mode domain and maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We first define the required control performance by fidelity, degree of coherence and purity in terms of the uncertainty of the Hamiltonian in Markovian open quantum system. By characterizing the required robustness using a sliding mode domain, a sampled-data design method is introduced for decoherence control in the quantum system. Furthermore, utilizing the sampled data, a control scheme has been designed on the basis of sliding mode control, and the choice of sampling operator and driving of quantum state during the sampling by the Lyapunov control method are discussed.
This paper presents a sampled-data approach for the robust decoherence control of a single qubit. The required robustness is defined using a sliding mode domain and the control law is designed offline and then utilized online with a single qubit having bounded uncertainties. Two classes of uncertainties are considered involving the system Hamiltonian and the coupling strength of the system-environment interaction. Three cases are analyzed in detail including amplitude damping decoherence, phase damping decoherence and depolarizing decoherence. Sampling periods are specifically designed for these cases to guarantee the required robustness. A sufficient condition is presented for guiding the design of unitary control for the case with amplitude damping decoherence. The proposed approach has potential applications in quantum error-correction and in constructing robust quantum gates.
This paper presents a sampled-data control approach based on sliding mode design for the robust control of a two-level quantum system, where the control law can be designed offline and then be used online for a quantum system with bounded uncertainties in the system Hamiltonian. Such a control law consists of a periodic sampling process and a Lyapunov control design. A sufficient condition on the relationships between related parameters in the control system is established and the Lyapunov control design is demonstrated by simulation, which can be used to show the required robustness of the quantum system in the presence of uncertainties.
This technical note presents a sampled-data approach to the robust control of a single qubit (quantum bit). The required robustness is defined using a sliding mode domain and the control law is designed offline and then utilized online with a single qubit having bounded uncertainties. Two classes of uncertainties are considered involving the system Hamiltonian and the coupling strength of the system-environment interaction. Four cases are analyzed in detail including without decoherence, with amplitude damping decoherence, phase damping decoherence and depolarizing decoherence. Sampling periods are specifically designed for these cases to guarantee the required robustness. Two sufficient conditions are presented for the design of a unitary control for the cases without decoherence and with amplitude damping decoherence. The proposed approach has potential applications in quantum error-correction and in constructing robust quantum gates.
Application of quantum measurement to control system plays an important role in quantum information processing or other field. Since any real system must interact with surrounding environment, one has to consider the quantum measurement and control about open system. This paper investigates the problem of robustness for a single qubit with operator errors, which enlarges the field of quantum robustness control. It establishes control models on the basis of sliding mode control under Markovian noise, and defines control performance with indices as fidelity; coherence and purity that have real physical meanings. According to the different control targets, this paper presents the corresponding sliding mode design and the analytical expression of the data sampling period in a concrete Markovian environment. Furthermore, based on sampled-data control law, tracking the fidelity, coherence and purity of system and so on different state performance index, realizes the effective control of the operator error caused by the return of the coherent effect.