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Chinese Physics B

One step to generate quantum controlled phase-shift gate using a trapped ion

Zhang Shi-jun, Chi Ma, Wen‐Hai Zhang, Ye Liu

Published May 1, 2008• 2 citations
Publisher

Abstract

This paper presents a very simple scheme for generating quantum controlled phase-shift gate with only one step by using the two vibrational modes of a trapped ion as the two qubits. The scheme couples two vibration degrees of freedom coupled with a suitable chosen laser excitation via the ionic states.
DOI
10.1088/1674-1056/17/5/010

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We propose a scheme to implement two-qubit controlled quantum phase gate(CQPG) via a single trapped two-level ion located in the standing wave field of a quantum cavity, in which the trap works beyond the Lamb–Dicke limit. When the light field is resonant with the atomic transition |g > ↔ |e> of the ion located at the antinode of the standing wave, we can perform CQPG between the internal and external states of the trapped ion; while the frequency of the light field is chosen to be resonant with the first red sideband of the collective vibrational mode of the ion located at the node of the standing wave, we can perform CQPG between the cavity mode and the collective vibrational mode of the trapped ion. Neither the Lamb–Dicke approximation nor the assistant classical laser is needed. Also we can generate a GHZ state if assisted with a classical laser.
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 describe how two vibrational degrees of freedom of a single trapped ion can be coupled through the action of suitably chosen laser excitation. We concentrate on a two-dimensional ion trap with dissimilar vibrational frequencies in the xxx and yyy directions of motion and derive from first principles a variety of quantized two-mode couplings, concentrating on a linear coupling that takes excitations from one mode to another. We demonstrate how this can result in a state rotation, in which it is possible to transfer the motional state of the ion from, say, the xxx direction to the yyy direction without prior knowledge of that motional state.
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We show that, under certain conditions, the two-qubit controlled-NOT logic operations can be realized exactly using one laser pulse. The target qubit and the control qubit are encoded by the internal and external degrees of freedom of a single trapped ion. The multiquantum process of the interaction between the internal and external degrees of freedom of the ion is considered. This scheme neither requires the cooled ion in its vibrational ground state nor necessitates performance of the Lamb-Dicke approximation.