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arXiv:1201.1339 · Quantum Information and Computation

One-step implementation of the Fredkin gate via quantum Zeno dynamics

Zhi‐Cheng Shi, Yan Xia, Jie Song, He-Shan Song

Published Mar 1, 2012• 10 citations
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Abstract

We study one-step implementation of the Fredkin gate in a bi-modal cavity under both resonant and large detuning conditions based on quantum Zeno dynamics, which reduces the complexity of experiment operations. The influence of cavity decay and atomic spontaneous emission is discussed by numerical calculation. The results demonstrate that the fidelity and the success probability are robust against cavity decay in both models and they are also insensitive to atomic spontaneous emission in the large detuning model. In addition, the interaction time is rather short in the resonant model compared to the large detuning model.

DOI
10.26421/qic12.3-4-3

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We present two efficient methods for implementing the Fredkin (controlled swap) gate with atoms separately trapped in an array of three high-QQQ coupled cavities. The first proposal is based on large detuning interaction that the effective long-distance dipole-dipole-like interaction between two distributed target qubits is achieved by virtually excited qubits and cavities. The second one utilizes the selective resonant dynamics, which leads to a fast resonant interaction in a certain subspace while leaving others unchanged. Both schemes can achieve the standard form of the Fredkin gate in a single step without any subsequent single-qubit operation. The effects of decoherence on the performance of the gate are also analyzed in virtue of master equation, and the strictly numerical simulation reveals the average fidelity of the quantum gate is relatively high corresponding to the state-of-the-art technology.
Based on the quantum Zeno dynamics, we propose two approaches for directly implementing a CNOT gate in a cavity QED system instead of constructing it from elementary gates. The first approach works in the decoherence-free subspaces (DFS) due to the quantum Zeno effect, which is robust against cavity decay. Based on the first model, we then propose the second approach which takes advantage of stimulated Raman adiabatic passage (STIRAP) with only six pulses; thus it is insensitive to the atomic spontaneous emission. The two schemes are suitable for different decoherence parameters. The strictly numerical simulation shows that the average gate fidelities for the two methods are relatively high.
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