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Physical Review A

Generation and replication of continuous-variable quadripartite cluster and Greenberger-Horne-Zeilinger states in four chains of superconducting transmission line resonators

Zhen Li, Sheng-li Ma, Zhipeng Yang, Aiping Fang, Pen-bo Li, Shaoyan Gao, Fuli Li

Published Apr 4, 2016• 7 citations
Publisher

Abstract

We consider a system consisting of four independent chains of coupled single-mode superconducting transmission line resonators and a gap-tunable qubit. When the first four resonators of the chains are coupled to the qubit properly driven by multicolor fields, we show that the resonators can be prepared in continuous-variable quadripartite cluster states via the decay of the qubit to its ground state. Moreover, the resulting cluster states can be replicated in the other resonators in column via the nearest-neighbor swapping interaction of the resonators. This means that one can generate a set of cluster states, each of which involves the four resonators from the different chains. By a similar protocol, we show that the generation and replication of continuous-variable quadripartite Greenberger-Horne-Zeilinger states in the chains of the resonators can be achieved. The numerical simulation shows that the present scheme is realizable in current accessible on-chip quantum circuit experiments. The present result may have a potential application for the realization of a large-scale one-way quantum computation.

DOI
10.1103/physreva.93.042305

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We propose a dissipative scheme for one-step generation of continuous-variable quadripartite cluster states in a circuit QED setup consisting of four superconducting coplanar waveguide resonators and a gap-tunable superconducting flux qubit. With external driving fields to adjust the desired qubit-resonator and resonator-resonator interactions, we show that continuous-variable quadripartite cluster states of the four resonators can be generated with the assistance of energy relaxation of the qubit. By comparison with the previous proposals, the distinct advantage of our scheme is that only one step of quantum operation is needed to realize the quantum state engineering. This makes our scheme simpler and more feasible in experiment. Our result may have useful application for implementing quantum computation in solid-state circuit QED systems.
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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.
Abstract Cluster states are essential quantum resources for one-way quantum computations and quantum networks. The reliable generation of cluster states in specific quantum systems is crucial for initializing complex quantum operations. In this paper, we introduce an efficient scheme for the deterministic preparation of a cluster state via circuit quantum electrodynamics (QED). Our scheme involves four individual microwave resonators, each of which is coupled to a superconducting transmon qutrit. We demonstrated that a four-cqubit cluster state can be achieved using three controlled-phase gate operations. The cluster state is prepared deterministically, eliminating the need for measurement-based feedback. Throughout these operations, the qutrit remains in its ground state, effectively minimizing decoherence from the qutrit. Numerical simulations suggest that our scheme can generate high-fidelity cluster states using current-circuit QED technology. We believe that our model will facilitate exploration of future large-scale continuous-variable quantum information processing systems.
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