One Lyapunov control for quantum systems and its application to entanglement generation

Yang, Wei

doi:10.1016/j.physleta.2013.01.040

Cited by 5 publications

(1 citation statement)

References 31 publications

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“…Quantum Lyapunov control was proposed as a good candidate for quantum state engineering. It has been well developed in both theory and applications in the last decades [14,[22][23][24][25][26][27][28][29][30][31]. The authors in Ref.…”

Section: Introductionmentioning

confidence: 99%

Realization of quantum gates by Lyapunov control

Hou

Wang

2014

Physics Letters A

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We propose a Lyapunov control design to achieve specific (or a family of) unitary time-evolution operators, i.e., quantum gates in the Schr\"{o}dinger picture by tracking control. Two examples are presented. In the first, we illustrate how to realize the Hadamard gate in a single-qubit system, while in the second, the controlled-NOT (CNOT) gate is implemented in two-qubit systems with the Ising and Heisenberg interactions. Furthermore, we demonstrate that the control can drive the time-evolution operator into the local equivalence class of the CNOT gate and the operator keeps in this class forever with the existence of Ising coupling.Comment: 9 pages, 5 figures. Physics Letters A (2014

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Section: Introductionmentioning

confidence: 99%

Realization of quantum gates by Lyapunov control

Hou

Wang

2014

Physics Letters A

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Optimal Lyapunov quantum control of two-level systems: Convergence and extended techniques

et al. 2014

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Taking a two-level system as an example, we show that a strong control field may enhance the efficiency of optimal Lyapunov quantum control in [Hou et al., Phys. Rev. A 86, 022321 (2012)] but could decrease its control fidelity. A relationship between the strength of the control field and the control fidelity is established. An extended technique, which combines free evolution and external control, is proposed to improve the control fidelity. We analytically demonstrate that the extended technique can be used to design a control law for steering a two-level system exactly to the target state. In such a way, the convergence of the extended optimal Lyapunov quantum control can be guaranteed.

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Lyapunov-Based Feedback Preparation of GHZ Entanglement of $N$ -Qubit Systems

Liu

Kuang

Cong

2017

IEEE Trans. Cybern.

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The Greenberger-Horne-Zeilinger (GHZ) entangled states are a typical class of entangled states in multiparticle systems and play an important role in the applications of quantum communication and quantum computation. For a general quantum system of qubits, degenerate measurement operators are often met, which cause the convergence obstacle in the state preparation or stabilization problem. This paper first generalizes the traditional quantum state continuous reduction theory to the case of a degenerate measurement operator and chooses a measurement operator for an arbitrarily given target GHZ entangled state, then presents a state stabilization control strategy based on the Lyapunov method and achieves the feedback preparation of the target GHZ state. In our stabilization strategy, we separate the target GHZ state and all the other GHZ states that often form the equilibrium points of the closed-loop system by dividing the state space into several different regions; and formally design a switching control law between the regions, which contains the control Hamiltonians to be constructed. By analyzing the stability of the closed-loop system in the different regions, we propose a systematic method for constructing the control Hamiltonians and solve the convergence problem caused by the degenerate measurement operator. The global stability of the whole closed-loop stochastic system is strictly proved. Also, we perform some simulation experiments on a three-qubit system and prepare a three-qubit GHZ entangled state. At the same time, the simulation results show the effectiveness of the switching control law and the construction method for the control Hamiltonians proposed in this paper.

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One Lyapunov control for quantum systems and its application to entanglement generation

Cited by 5 publications

References 31 publications

Realization of quantum gates by Lyapunov control

Realization of quantum gates by Lyapunov control

Optimal Lyapunov quantum control of two-level systems: Convergence and extended techniques

Lyapunov-Based Feedback Preparation of GHZ Entanglement of $N$ -Qubit Systems

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