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IEEE International Conference on Information and Automation (ICIA)

Adaptive robust control on the fidelity of a two-level quantum system in various environments

Juju Hu, Qiang Ke, Yinghua Ji

Published Aug 1, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.1109/icinfa.2016.7832025

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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.
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.
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.
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.
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 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.