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Journal of Modern Optics

Noise resistance of Toffoli gate in an array of coupled cavities

Li-Cong Song, Yan Xia, Jie Song

Published Jun 23, 2014• 8 citations
Publisher

Abstract

Two schemes of implementing the Toffoli gate are proposed in an array of coupled cavities. In the first one, two classical laser fields with fixed Rabi frequency are used via quantum Zeno dynamics. While in the second scheme, the invariant-based inverse engineering is used to implement the Toffoli gate, which can drive the instantaneous eigenstates to evolve exactly under the Schrödinger equation. The strictly numerical simulations are given and the influences of cavity decay and spontaneous emission on the Toffoli gate operation are analyzed with master equation. The result shows that our schemes for the Toffoli gate are robust against the decoherence because of the short time needed.

DOI
10.1080/09500340.2014.930194

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Two schemes of implementing the Toffoli gate are proposed in an array of coupled cavities. In the first one, two classical laser fields with fixed Rabi frequency are used via quantum Zeno dynamics. While in the second scheme, the invariant-based inverse engineering is used to implement the Toffoli gate, which can drive the instantaneous eigenstates to evolve exactly under the Schrödinger equation. The strictly numerical simulations are given and the influences of cavity decay and spontaneous emission on the Toffoli gate operation are analyzed with master equation. The result shows that our schemes for the Toffoli gate are robust against the decoherence because of the short time needed.
The Toffoli gate (controlled-controlled-NOT gate) is one typical three-qubit gate, it plus a Hadamard gate form a universal set of gates in quantum computation. We present an efficient method to implement the Toffoli gate using an array of coupled cavities with one three-level atom in each cavity. The large detuning between atoms and classical (quantum) fields plays an important role and the gate is implemented in one-step. The quantum information is encoded into the low-lying states of identical atoms and it is convenient to address qubit individually. Based on the Markovian master equation, it is shown that the scheme to implement the Toffoli gate is robust against the decoherence.
This paper proposes a scheme for realization of a three-qubit Toffoli gate operation using three four-level atoms by a selective atom-field interaction in a cavity quantum electrodynamics system. In the proposed protocol, the quantum information is encoded on the stable ground states of atoms, and atomic spontaneous emission is negligible as the large atom-cavity detuning effectively suppresses the spontaneous decay of the atoms. The influence of the dissipation on fidelity and success probability of the three-qubit Toffoli gate is also discussed. The scheme can also be applied to realize an N -qubit Toffoli gate and the interaction time required does not rise with increasing the number of qubits.
We propose a distributed quantum architecture (three atoms trapped in three coupled cavities) to construct an asymmetric spin 1/2 Heisenberg XY model. The effective atom–atom coupling is obtained with the cavity modes and the atomic excited states being virtually populated. We then demonstrate that the model can be used for implementing a three-qubit Toffoli gate with high fidelity. The feasibility and effectiveness of our scheme as well as the influences of decoherence effects (the atomic spontaneous emission and the cavity decay) on the gate fidelity are finally discussed. The scheme can be generalized for distributed quantum computation with the Heisenberg XY model.
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.