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arXiv:1111.5676 · Physical Review B

Fast generation of multiparticle entangled state for flux qubits in a circle array of transmission line resonators with tunable coupling

Zhihui Peng, Yu-xi Liu, Yasunobu Nakamura, Jaw-Shen Tsai

Published Jan 30, 2012• 22 citations
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Abstract

We study a one-step approach to the fast generation of Greenberger-Horne-Zeilinger (GHZ) states in a circuit QED system with superconducting flux qubits. The GHZ state can be generated in about 10 ns, which is much shorter than the coherence time of flux qubits and comparable with the time of single-qubit operation. In our proposal a time-dependent microwave field is applied to a superconducting transmission line resonator (TLR) and displaces the resonator in a controlled manner, thus inducing indirect qubit-qubit coupling without residual entanglement between the qubits and the resonator. The design of a tunably coupled TLR circle array provides us with the potential for extending this one-step scheme to the case of many qubits coupled via several TLRs.

DOI
10.1103/physrevb.85.024537

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We study a one-step approach to the fast generation of Greenberger-Horne-Zeilinger (GHZ) states in a circuit QED system with superconducting flux qubits. The GHZ state can be generated in about 10 ns, which is much shorter than the coherence time of flux qubits and comparable with the time of single-qubit operation. In our proposal a time-dependent microwave field is applied to a superconducting transmission line resonator (TLR) and displaces the resonator in a controlled manner, thus inducing indirect qubit-qubit coupling without residual entanglement between the qubits and the resonator. The design of a tunably coupled TLR circle array provides us with the potential for extending this one-step scheme to the case of many qubits coupled via several TLRs.
Quantum entanglement is an important resource for quantum information processing tasks. However, realistic multipartite entangled state production is very difficult. In this paper, we propose an efficient single-step scheme for generating many body Greenberger–Horne–Zeilinger (GHZ) states on superconducting circuits by using a superconducting transmission-line resonator (TLR) interact with [Formula: see text] superconducting transmon qubits. The distinct merit of our proposal is that it does not require the qubit-resonator coupling strengths to be the same, which is usually impractical experimentally, and thus is one of the main reasons for entanglement generation infidelity in previous single-step schemes. The removing of the uniform interaction requirement is achieved by modulating the qubits splitting frequencies with ac microwave fields, which results in tunable individual qubit-resonator coupling strength, and thus effective uniform qubit–qubit interaction Hamiltonian can be obtained. Since microwave control is conventional nowadays, our proposal can be directly tested experimentally, which makes previous multipartite entangled states generation schemes more efficient.
Although the multi-level structure of superconducting qubits may result in calculation errors, it can be rationally used to effectively improve the speed of gate operations. Utilizing a current-biased Josephson junction (λ-type rf-SQUID) as a tunable coupler for superconducting transmission line resonators (TLRs), under the large detuning condition, we demonstrate the controllable generation of entangled coherent states in circuit quantum electrodynamics (circuit QED). The coupling between the TLRs and the qubit can be effectively regulated by an external bias current or coupling capacitor. Further investigations indicate that the maximum entangled state can be obtained through measuring the excited state of the superconducting qubits. Then, the influence of the TLR decay on the prepared entangled states is analyzed.
Abstract The optimal generation of entangled states is of significance to information processing and state engineering. Here, an efficient scheme is proposed for creating entangled states between two superconducting qubits in a circuit quantum electrodynamics (QED). The two qubits that resonantly interact with a common cavity mode of transmission‐line resonator (TLR) can be effectively coupled by the data bus of the microwave resonator. By the invariant‐based shortcuts to adiabaticity (STA), two types of maximally entangled states can be controllably induced only by adjusting the Rabi drivings. Based on the resonant drivings with constant rates, the shortcut strategy is capable of implementing faster operations when compared with the dispersive approach. The fidelities are highly robust against the decoherence effects and the instabilities of Rabi rates. Thus the proposal could offer a potential route toward the entanglement generations in an optimized manner.
We propose a one-step method to prepare multi-qubit GHZ and W states with transmon qubits capacitively coupled to a superconducting transmission line resonator (TLR). Compared with the scheme firstly introduced by Wang et al. [ Phys. Rev. B 81 (2010) 104524 ], our schemes have longer dephasing time and much shorter operation time because the transmon qubits we used are not only more robust to the decoherence and the unavoidable parameter variations, but also have much stronger coupling constant with TLR. Based on the favourable properties of transmons and TLR, our method is more feasible in experiment.
We propose a circuit quantum electrodynamics (QED) realization of a protocol to generate a Greenberger-Horne-Zeilinger (GHZ) state for NNN superconducting transmon qubits homogeneously coupled to a superconducting transmission line resonator in the dispersive limit. We derive an effective Hamiltonian with pairwise qubit exchange interactions of the XYXYXY type, $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}(XX+YY)$, that can be globally controlled. Starting from a separable initial state, these interactions allow us to generate a multi-qubit GHZ state within a time ${t}_{\mathrm{GHZ}}\ensuremath{\sim}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}}^{\ensuremath{-}1}$. We discuss how to probe the nonlocal nature and the genuine NNN-partite entanglement of the generated state. Finally, we investigate the stability of the proposed scheme to inhomogeneities in the physical parameters.