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International Journal of Control

Further results on sampled-data design for robust control of a single qubit

Yuanlong Wang, Chunlin Chen, Daoyi Dong

Published Mar 3, 2014• 6 citations
Publisher

Abstract

This paper presents further results on the robust control method for qubit systems in Dong et al. (2013) Dong, D., Petersen, I.R., & Rabitz, H. (2013). Sampled-data design for robust control of a single qubit. IEEE Transactions on Automatic Control, 58, 2654–2659.[Crossref], [Web of Science ®] , [Google Scholar]. Based on the properties of an antisymmetric system, an alternative method is presented to analyse and exclude singularity intervals in the proof of partial original results. For the case of amplitude damping decoherence, a larger sampling period is presented when the upper bound of the probability of failure is small enough. For the case of phase damping decoherence, a larger sampling period is given when the lower bound of the target coherence is large enough. Furthermore, we provide improved sampling periods for amplitude damping decoherence and phase damping decoherence without the above prior constraints.

DOI
10.1080/00207179.2014.899713

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This paper presents further results on the robust control method for qubit systems in Dong et al. (2013) Dong, D., Petersen, I.R., & Rabitz, H. (2013). Sampled-data design for robust control of a single qubit. IEEE Transactions on Automatic Control, 58, 2654–2659.[Crossref], [Web of Science ®] , [Google Scholar]. Based on the properties of an antisymmetric system, an alternative method is presented to analyse and exclude singularity intervals in the proof of partial original results. For the case of amplitude damping decoherence, a larger sampling period is presented when the upper bound of the probability of failure is small enough. For the case of phase damping decoherence, a larger sampling period is given when the lower bound of the target coherence is large enough. Furthermore, we provide improved sampling periods for amplitude damping decoherence and phase damping decoherence without the above prior constraints.
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 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.
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.
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.
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.
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.