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Chinese Physics B

Unconventional geometric phase gate and multiqubit entanglement for hot ions with a frequency-modulated field

Wenxue Zhong, Guangling Cheng, Aixi Chen

Published Nov 1, 2010• 16 citations
Publisher

Abstract

We present an alternative scheme for implementing the unconventional geometric two-qubit phase gate and preparing multiqubit entanglement by using a frequency-modulated laser field to simultaneously illuminate all ions. Selecting the index of modulation yields selective mechanisms for coupling and decoupling between the internal and the external states of the ions. By the selective mechanisms, we obtain the unconventional geometric two-qubit phase gate, multiparticle Greenberger—Horne—Zeilinger states and highly entangled cluster states. Our scheme is insensitive to the thermal motion of the ions.

DOI
10.1088/1674-1056/19/11/110310

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We present an alternative scheme for implementing the unconventional geometric two-qubit phase gate and preparing multiqubit entanglement by using a frequency-modulated laser field to simultaneously illuminate all ions. Selecting the index of modulation yields selective mechanisms for coupling and decoupling between the internal and the external states of the ions. By the selective mechanisms, we obtain the unconventional geometric two-qubit phase gate, multiparticle Greenberger—Horne—Zeilinger states and highly entangled cluster states. Our scheme is insensitive to the thermal motion of the ions.
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.
We propose a scheme for the realization of unconventional geometric two-qubit phase gates with two identical two-level ions. In the present scheme, the two ions are simultaneously illuminated by a standing-wave laser pulse with its pulse frequency being tuned to the ionic transition. The gate operation time can be much shorter, making the system robust against decoherence. In addition, we choose the appropriate experimental parameters to construct the geometric phase gate in one step, and thus avoid implementing the pure geometric single qubit operation.
A robust scheme is proposed for producing maximally entangled states for many trapped ions in thermal motion. In the scheme the ions are simultaneously illuminated by two standing-wave laser fields. During the operation the phases of the lasers are inverted, which not only cancels the vibration-dependent parts in the evolution operator, but also suppresses direct off-resonant coupling of the internal states. Thus, our scheme allows the production of entanglement for hot trapped ions with laser fields of high intensity, which makes the entanglement speed extremely high.
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.
We show that an unconventional geometric phase gate between an arbitrary pair of distant qubits in a two-dimensional network can be obtained. In the scheme, the off-resonant Raman transitions between two ground states of the trapped atoms, which, induced by the cavity modes and external fields, can lead to selective qubit–qubit coupling. As a typical application, this interaction mechanism can be used to realize unconventional geometric phase gates. The advantage of the proposed scheme is that the atomic spontaneous emission is effectively suppressed, which makes the scheme very robust against decoherence.