One-step implementation of the genuine Fredkin gate in high-$Q$ coupled three-cavity arrays

TL;DR

This paper proposes two efficient one-step methods for implementing the Fredkin gate in high-Q coupled three-cavity arrays, achieving high fidelity without additional single-qubit operations.

Contribution

It introduces resonant and dispersive interaction schemes for direct Fredkin gate implementation in cavity arrays, avoiding multi-step procedures.

Findings

Both schemes realize the Fredkin gate in a single step.

Numerical simulations show high average fidelity under decoherence.

The methods are feasible for high-Q cavity systems.

Abstract

We present two efficient methods for implementing the Fredkin gate with atoms separately trapped in an array of three high-$Q$ coupled cavities. The first proposal is based on the resonant dynamics, which leads to a fast resonant interaction in a certain subspace while leaving others unchanged, and the second one utilizes a dispersive interaction such that the effective long-distance dipole-dipole interaction between two distributed target qubits is achieved by virtually excited process. 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 that the average fidelity of the quantum gate is high.