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Chinese Physics

A scheme for the implementation of unconventional geometric phase gates with trapped ions

Hong Xie, LI Hong-cai, Rong‐Can Yang, Lin Xiu, Zhiping Huang

Published Nov 1, 2007• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/16/11/039

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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.
We propose a scheme to generate a quantum phase gate via an unconventional geometric phase shift in an ion-trap system.Since the gate time is only related to the frequency of the vibrational mode, the present scheme, based on the resonant interaction of the trapped ions with a standing-wave laser beam, requires a much shorter gate time than the scheme based on the resonant interaction of the atoms and the cavity.Also the heating effect of the vibrational mode is negligible under certain conditions.
We suggest a fast two-qubit quantum logic gates for trapped ions in thermal motion via geometric phase shifts. In the scheme, several vibrational modes are simultaneously displaced by driving the ions with a single off-resonant standing-wave laser. Under certain conditions, all the vibrational modes simultaneously return to the original points in the phase spaces along corresponding closed paths depending on the electronic states, producing a geometric phase gate. During the gate operation, the ions undergo no electronic transitions and the gate time might be shorter than the period of the center-of-mass vibration.
We propose a geometric phase gate in a decoherence-free subspace with trapped ions. The quantum information is encoded in the Zeeman sublevels of the ground state and two physical qubits to make up one logical qubit with ultra-long coherence time. Single- and two-qubit operations together with the transport and splitting of linear ion crystals allow for a robust and decoherence-free scalable quantum processor. For the ease of the phase gate realization we employ one Raman laser field on four ions simultaneously, i.e. no tight focus for addressing. The decoherence-free subspace is left neither during gate operations nor during the transport of quantum information.
Based on squeezed operators this paper has implemented an ideal unconventional geometric quantum gate (GQG) in ion trap-optical cavity system by radiating the trapped ions with the cavity field of frequency ω c and an external laser field of frequency ωL. It can ensure that the gate time is shorter than the coherence time for qubits and the decay time of the optical cavity by appropriately tuning the ionic transition frequency ω 0 , the frequencies of the cavity mode ω c and the vibrational mode ν. It has also realized the unconventional GQG under the influence of the cavity decay based on the squeezed-like operators and found that the present scheme works well for the smaller cavity decay by investigating the corresponding fidelity and success probability.
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.