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IEEE International Conference on Information and Automation (ICIA)

Sampled-Data design for robust decoherence control of Markovian open quantum system

Yinghua Ji, Qiang Ke, Juju Hu

Published Jul 1, 2017• 0 citations
Publisher

Abstract

Quantum robust control has been recognized as a critical issue in quantum systems, since many quantum systems are unavoidably subject to disturbances and uncertainties in practical applications. Considered uncertainty of Hamiltonian in the Markovian quantum system, on one hand this paper define the control effect based on fidelity, purity and degree of coherence, on the other hand design control scheme and acquire the corresponding analytical expression of sampling period based on data sampling. Meanwhile the author discuss about selection of sampling operator and quantum state driven in the process of quantum sampling.

DOI
10.1109/icinfa.2017.8078966

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Quantum robust control has been recognized as a critical issue in quantum systems, since many quantum systems are unavoidably subject to disturbances and uncertainties in practical applications. Considered uncertainty of Hamiltonian in the Markovian quantum system, on one hand this paper define the control effect based on fidelity, purity and degree of coherence, on the other hand design control scheme and acquire the corresponding analytical expression of sampling period based on data sampling. Meanwhile the author discuss about selection of sampling operator and quantum state driven in the process of quantum sampling.
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Superconducting quantum systems are promising candidates for quantum information processing due to their scalability and design flexibility. However, real quantum systems usually suffer from decoherence caused by environment disturbance. This effect, together with parametric error and un-modelled dynamics, usually leads to uncertainties in system models, which will destroy the system's excellent quantum properties. Therefore, it is significant to study robust control of open quantum system to enhance control performance in reality. In this paper, the control effect based on fidelity of the required robustness is defined using the concept of a sliding mode domain by considering uncertainties. Then, we design control scheme and acquire the corresponding analytical expression of sampling period based on data sampling. Meanwhile, we discuss the selection of sampling operator and quantum state drive in the process of quantum sampling. Furthermore, the influences of coupling constant, cut-off frequency and temperature on the sampling period are analysed.
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.
Quantum control is responsible for many key problems in quantum information processing such as engineering quantum state and quantum gate, suppressing decoherence, etc. The research on quantum control will greatly advance the development of quantum information science. The uncertainties exist in quantum systems also causes decoherence, which will destroy systems' excellent quantum properties. Hence it is significant to study robust control of open quantum system to enhance control performance in reality. In this paper, based on the robust control method for quantum systems, we investigate robustness control strategies against uncertainties under three classical environments by taking an eigenstate of the two-level quantum system as a sliding mode, and acquire the corresponding analytical expression of sampling period based on data sampling. Furthermore, the influences of temperature and squeezing parameter on the sampling period are analyzed.
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.