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Laser Physics Letters

The preparation of a Bell entangled state using superconducting qubits via Lyapunov control

Cui-Yu Zhang, Mao-Fa Fang

Published May 1, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1612-202x/add4ec

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Abstract We present a scheme for the dissipative preparation of an entangled steady state between two atomic qubits separately trapped in the coupled cavities. The combination of coherent driving fields and dissipative processes will drive the system into a steady state. By choosing different frequency of classical laser field, the target steady state can be generated in different ways. In our scheme, the atomic spontaneous emission and the cavity decay can be used as a prerequisite. The numerical simulation shows that the maximally entangled state with high fidelity and purity can be produced regardless of the initial state. The fidelity is insensitive to the fluctuation of the system parameters.
We present a scheme for the dissipative preparation of an entangled steady state of two superconducting qubits in a circuit quantum electrodynamics (QED) setup. Combining resonator photon loss---a dissipative process already present in the setup---with an effective two-photon microwave drive, we engineer an effective decay mechanism which prepares a maximally entangled state of the two qubits. This state is then maintained as the steady state of the driven, dissipative evolution. The performance of the dissipative state preparation protocol is studied analytically and verified numerically. In view of the experimental implementation of the presented scheme we investigate the effects of potential experimental imperfections and show that our scheme is robust to small deviations in the parameters. We find that high fidelities with the target state can be achieved both with state-of-the-art three-dimensional, as well as with the more commonly used two-dimensional transmons. The promising results of our study thus open a route for the demonstration of a highly entangled steady state in circuit QED.
We show that simulated relativistic motion can generate entanglement between artificial atoms and protect them from spontaneous emission. We consider a pair of superconducting qubits coupled to a resonator mode, where the modulation of the coupling strength can mimic the harmonic motion of the qubits at relativistic speeds, generating acceleration radiation. We find the optimal feasible conditions for generating a stationary entangled state between the qubits when they are initially prepared in their ground state. Furthermore, we analyse the effects of motion on the probability of spontaneous emission in the standard scenarios of single-atom and two-atom superradiance, where one or two excitations are initially present. Finally, we show that relativistic motion induces sub-radiance and can generate a Zeno-like effect, preserving the excitations from radiative decay.