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Communications in Theoretical Physics

One-Step Generation of Multi-Qubit GHZ and W States in Superconducting Transmon Qubit System

Gui-Long Gao, Gen-Chang Cai, Shou-Sheng Huang, Mingfeng Wang, Nian-Quan Jiang

Published Feb 1, 2012• 3 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/57/2/07

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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.
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.
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.