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Journal of the Optical Society of America B

An unconventional geometric phase gate between two arbitrary qubits in a two-dimensional network

Zhi‐Rong Zhong, Xiaobin Huang

Published Jan 12, 2015• 4 citations
Publisher

Abstract

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.

DOI
10.1364/josab.32.000258

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In this paper, we propose a scheme for implementing an unconventional two-qubit geometric phase gate for two distant atoms trapped in cavities connected by an optical fiber. During the gate operation, the atoms are still in the ground states, while the cavity modes and fiber mode are displaced along a circle in the phase space. In this way, the system can acquire different geometric phases conditional upon the atomic states. We find that the operation of the geometric phase gate can be speeded up as the detuning between the cavity field and light fields decreases. Moreover, it is observed that the fidelity for the geometric phase gate is remarkably insensitive to the fluctuation of the detuning parameter. The effects of cavity decay and fiber loss on the gate have also been checked.
In this paper, we present a scheme for implementing the unconventional geometric two-qubit phase gate with nonzero dynamical phase based on two-channel Raman interaction of two atoms in a cavity. We show that the dynamical phase and the total phase for a cyclic evolution are proportional to the geometric phase in the same cyclic evolution; hence they possess the same geometric features as does the geometric phase. In our scheme, the atomic excited state is adiabatically eliminated, and the operation of the proposed logic gate involves only the metastable states of the atoms; thus the effect of the atomic spontaneous emission can be neglected. The influence of the cavity decay on our scheme is examined. It is found that the relations regarding the dynamical phase, the total phase, and the geometric phase in the ideal situation are still valid in the case of weak cavity decay. Feasibility and the effect of the phase fluctuations of the driving laser fields are also discussed.
Using two cyclic three-level artificial atoms, we propose a scheme for realizing two-qubit quantum phase gates via an unconventional geometric phase shift in a cavity. In this scheme, the excited states of the two artificial atoms are adiabatically eliminated, and the logical gates' operation only involves their metastable states. Moreover, under certain conditions, the artificial atoms are disentangled with the cavity mode. Thus the gate is insensitive to both the cavity decay and the spontaneous emission of the artificial atoms.
We propose a scheme for implementing unconventional geometric quantum computation by using the interaction of two atoms with a two-mode cavity field. The evolution of the system results in a nontrivial two-qubit phase gate. The operation of the proposed gate involves only metastable states of the atom and hence is not affected by spontaneous emission. The effect of cavity decay on the gate is investigated. It is shown that the evolution time of the gate in the two-mode case is less than that in the single-mode case proposed by Feng et al. [Phys. Rev. A 75, 052312 (2007)]. Thus the gate can be more decay tolerant than the previous one. The scheme can also be generalized to a system consisting of two atoms interacting with an NNN-mode cavity field.