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Physical Review A

Quantum computing with trapped ions in an optical cavity via Raman transition

Mang Feng

Published Nov 21, 2002• 45 citations
Publisher

Abstract

In the system with ions confined both in a linear trap and in a high-$Q$ single-mode optical cavity, a quantum computing scheme is proposed by using lasers and quantized cavity field, via Raman transition. A controlled-NOT gate with reduced operations can be performed on two non-neighboring ions without the involvement of both motional states of ions and cavity mode. Experimental feasibility of achieving our scheme is discussed.

DOI
10.1103/physreva.66.054303

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In the system with ions confined both in a linear trap and in a high-QQQ single-mode optical cavity, a quantum computing scheme is proposed by using lasers and quantized cavity field, via Raman transition. A controlled-NOT gate with reduced operations can be performed on two non-neighboring ions without the involvement of both motional states of ions and cavity mode. Experimental feasibility of achieving our scheme is discussed.
In the system with ions confined both in a linear trap and in a high-QQQ single mode cavity, we present a simple quantum computing scheme by means of lasers and quantized cavity field, based on a previous proposal with bichromatic radiation [Phys. Rev. Lett. 82,82,82, 1971 (1999)]. The controlled-NOT gate operation can be performed by only three operations and it is independent of motional states of ions. Experimental feasibility for achieving our scheme is discussed.
We propose a scheme to perform basic gates of quantum computing and prepare entangled states in a system with cold trapped ions located in a single-mode optical cavity. General quantum computing can be done with both the motional state of the trapped ion and cavity state being qubits. We can also generate different kinds of entangled states in such a system without state reduction, and can transfer quantum states from an ion in one trap to an ion in another trap. The experimental requirements for achieving our scheme are discussed.
In the system with a two-level ion confined both in a linear trap and in a high-Q single-mode cavity, we present a simple scheme to realize the basic two-qubit logic gates such as the quantum phase gate (QPG), the SWAP gate and the controlled-NOT (CNOT) gate beyond the Lamb–Dicke (LD) limit. We realize the three kinds of two-qubit quantum phase gates, i.e. QPG operation involving the cavity mode as well as the vibrational mode of the trapped ion, QPG operation involving the internal states as well as the vibrational mode of the trapped ion and QPG operation involving the internal states of the trapped ion as well as the cavity mode. The controlled-NOT gate can be implemented from a QPG operation through a rotation of the second qubit before and after the QPG operation. We can also perform the SWAP gate operation involving the ionic internal states of the trapped ion and the two-mode bosonic basis. The logic gates involving the cavity mode as well as the vibrational mode of the trapped ion are insensitive to spontaneous emission, and the logic gates involving the internal states as well as the vibrational mode of the trapped ion are insensitive to the decay of the cavity, which is an important feature for the practical implementation of quantum computing. Neither the LD approximation nor the auxiliary atomic level is needed in our scheme. Experimental feasibility for achieving our scheme is also discussed.
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.
In the system with two two-level ions confined in a linear trap, this paper presents a simple scheme to realize the quantum phase gate (QPG) and the swap gate beyond the Lamb–Dicke (LD) limit. These two-qubit quantum logic gates only involve the internal states of two trapped ions. The scheme does not use the vibrational mode as the data bus and only requires a single resonant interaction of the ions with the lasers. Neither the LD approximation nor the auxiliary atomic level is needed in the proposed scheme. Thus the scheme is simple and the interaction time is very short, which is important in view of decoherence. The experimental feasibility for achieving this scheme is also discussed.