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Physica Scripta

A fast scheme for one-step preparation of a highly entangled cluster state in the ion-trap system

Ying-Qiao Zhang, Shou Zhang, Jin Xing-Ri

Published Nov 20, 2008• 2 citations
Publisher

Abstract

We propose to implement a highly entangled cluster state (HECS) with only one step based on the resonant interactions among N two-level ions and two different standing-wave lasers with a phase difference of π/2. The time for preparation of the HECS is related only to the frequency of the vibrational mode ν (i.e. t=2π/ν). We can ensure that the preparation time is short enough by setting the larger vibrational mode frequency ν to neglect the effect of the decoherence of the qubits. During the process of preparing the HECS, the heating effect of the vibrational mode can be neglected and the initial qubits need only one evolution with the time interval t. The reduced operation steps and the shorter preparation time make the present scheme more feasible in experiments.

DOI
10.1088/0031-8949/78/06/065401

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We propose to implement a highly entangled cluster state (HECS) with only one step based on the resonant interactions among N two-level ions and two different standing-wave lasers with a phase difference of π/2. The time for preparation of the HECS is related only to the frequency of the vibrational mode ν (i.e. t=2π/ν). We can ensure that the preparation time is short enough by setting the larger vibrational mode frequency ν to neglect the effect of the decoherence of the qubits. During the process of preparing the HECS, the heating effect of the vibrational mode can be neglected and the initial qubits need only one evolution with the time interval t. The reduced operation steps and the shorter preparation time make the present scheme more feasible in experiments.
Three experimentally feasible schemes are proposed for generating multipartite entangled states of cold trapped ions.In the first scheme,a GHZ state can be simply synthesized in a single step. The second scheme is to prepare fully symmetric W states with two steps.The third scheme describes the sequential generation of linear cluster states.In addition,a method to create a larger cluster state was also presented by fuzing the end qubits of two smaller cluster states in order to decrease the distortion caused by decoherence,which can speed up the generation of large cluster states.The above schemes involve the collective interaction between multiple ions with the vibrational ground state and a large detuned laser. Compared with previous schemes,the above schemes have four advantages.Firstly,they do not require the vibrational mode of ions as memory.Secondly,they do not need to address the ions individually.Thirdly, they are free from the effects of phase fluctuation of laser field.Finally,they need less operations.
We propose an alternative scheme for preparing N-qubit cluster state by using a frequency-modulated laser field to simultaneously illuminate the trapped ions. Selecting the index of modulation yields the selective mechanisms of coupling and decoupling between the internal and external states of the ions. Based on the selective mechanisms, the highly entangled cluster state is achieved. In our scheme, the vibration mode is only virtually excited. Thus the quantum operations are insensitive to the heating and lead to the high-fidelity quantum information processing.
An alternative scheme is proposed for one-step generation of multiparticle cluster state with trapped ions in thermal motion. In this scheme, the ions are simultaneously illuminated by a standing-wave laser tuned to the carrier. During the operations, the vibrational mode is virtually excited, thus the quantum operations are insensitive to the heating. It is shown that the high fidelity multiparticle entanglement could be generated in just one step even including the small fluctuations of parameters. In addition, the ion does not need to be exactly positioned at the node of the standing wave, which is also important from the viewpoint of experiment.
In this paper, based on the recent experiment by Roos et al. [Science 304, 1478 (2004)], a theoretical scheme is proposed to create the multipartite entanglement of many trapped ions and implement a two-qubit quantum phase gate between two ions in ion trap. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. We also show that the scheme can be used to directly transfer information between two ions. The scheme has the advantage that it does not use the vibrational mode as the data bus and only requires a single resonant interaction. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed. In view of the decoherence mechanism, the simplification for the entangled state preparation and experimental implementation of quantum logic operation may become crucial.
Following the recent proposal by Briegel et al. [Phys. Rev. Lett. 86 (2001) 910], a procedure is proposed for one-step realizing quantum control phase gates with two trapped ions in thermal motion. It is shown that the scheme can also be used to create a new special type of entangled states, i.e., cluster states of many trapped ions. In the scheme the two-trapped ions are simultaneously excited by a single laser beam and the frequency of the laser beam is slightly off resonance with the first lower vibration sideband of the trapped ions. The distinct advantage of the scheme is that it does not use the vibrational mode as the data bus. Furthermore, our scheme is insensitive to both the initial motional state and heating (or decay) as long as the system remains in the Lamb–Dicke regime.