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Advanced Quantum Technologies

Generation of W States in Waveguide‐Coupled Emitters Via Lyapunov Control

Du Ran, Shuai Liu, Zelong He, Peng‐Yu Su, Suihu Dang, Ya-dong Li, Chun‐lei Du

Published May 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT We propose a scheme for preparing a three‐qubit W state in a half‐waveguide emitter system using Lyapunov control. The system comprises three two‐level emitters coupled to a mirror‐terminated one‐dimensional waveguide. Lyapunov control is realized by engineering time‐dependent driving fields that steer the system toward the target W state and decrease in amplitude as the system approaches the target. Both local control with individually addressed emitters and global control with a uniform drive are considered. Numerical simulations show that near‐unit target‐state population is achieved under both control strategies, with faster convergence under local control. Robustness is further examined under parameter variations, imperfect initialization, and dissipation. The results support Lyapunov control as an efficient approach to on‐demand multipartite entanglement generation in waveguide‐based quantum networks.

DOI
10.1002/qute.70302

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Abstract We investigate how to prepare a Bell entangled state deterministically by using two remote superconducting qubits coupled to a coplanar waveguide resonator via Lyapunov control. The results show that when spontaneous emission of the qubits is not considered, the qubits can be completely driven to the Bell entangled state by the control fields, while the spontaneous emission of the qubits is considered, the fidelity between the prepared state and the Bell entangled state can still reach a high value even in the case with a relatively large spontaneous emission rate in qubits. We also find that stronger control fields can accelerate the evolution of the state from the initial state to the Bell entangled state. In addition, there is no doubt that the larger spontaneous emission would lead to faster decoherence, which will accelerate the system to reach the target steady state. In other words, our scheme provides an efficient way for the preparation of entangled states in superconducting systems.
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In this paper, we propose a scheme for the entanglement creations and the quantum gate implementations of spin qubits via Lyapunov control. We first show that three types of Bell states can be generated in one step with the traditional Lyapunov control. After that, the traditional Lyapunov control is generalized with the design of two Lyapunov functions that characterize the distance between two unitary operators. Thus, the Lyapunov control can be also used in constructing desired unitary operations. The performance of the entanglement creations and the quantum gate implementations are both estimated via numerical simulations. The results show the scheme holds robustness against the errors of the fields and couplings. As the generalization of Lyapunov control can not only be used in spin systems, the scheme may benefit the quantum information processing in different quantum systems.
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