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Chinese Journal of Quantum Electronics

Implementing quantum controlled phase gates with trapped ions

NI Zhi-xiang

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

A scheme for implementing three-qubit quantum controlled phase gate is proposed in the trap-ion system.It only requires the resonant interaction between trapped ions and lasers.Compared to the scheme in other papers,the steps needed are much less.In addition,the scheme doesn't need any type of measurement.

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A trapped ion in a cavity can simultaneously interact with a laser field as well as the cavity field. Based on the point, we propose a new scheme to implement quantum logic gates such as single qubit rotation gate, two qubit controlled-phase gate and controlled-NOT gate. and scheme employs the model used in literature [10-12] and is different from these works because computation basis is composed by the internal ionic state and motional state. We also discussed the experimental requirement for our scheme.
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 superposition of motional coherent states with arbitrary coefficients on a line in phase space and implement a quantum controlled phase-gate for multiple trapped ions with a single standing-wave laser pulse whose carrier frequency is tuned to the ions transition. In the scheme each ion does not need to be exactly positioned at the node of the standing wave, which is very important from viewpoint of experiment. Furthermore, our scheme may allow the generation of a superposition of coherent states with large mean phonon number for a large number of trapped ions in a fast way by choosing suitable laser intensity. We show that it can also be used to generate maximally entangled states of multiple trapped ions.