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Implementing the genuine Fredkin gate in an array of coupled cavities

Xiao-Qiang Shao, Tai-Yu Zheng, Zhang Shou, C. H. Oh

Published Sep 4, 2013• 0 citations
OpenAlex

Abstract

We present two efficient methods for implementing the Fredkin (controlled swap) gate with atoms separately trapped in an array of three high-$Q$ 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.

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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.
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 an effective long-distance dipole–dipole interaction between two distributed target qubits is achieved by a 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 the master equation, and strictly numerical simulation reveals that the average fidelity of the quantum gate is high.
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.
We propose a one-step scheme to implement a multiqubit controlled phase gate with one qubit simultaneously controlling multiple qubits with three-level atoms at distant nodes in coupled cavity arrays. Selective qubit-qubit couplings are achieved by adiabatically eliminating the atomic excited states and photonic states, and the required phase shifts between the control qubit and any target qubit can be realized through suitable choices of the parameters of the external fields. Moreover, the effective model is robust against decoherence because neither the atoms nor the field modes are excited during the gate operation, leading to a useful step toward scalable quantum computing networks.
In a recent remarkable experiment [Sci. Adv. 2, e1501531 (2016)], a 3-qubit quantum Fredkin (i.e., controlled-SWAP) gate was demonstrated by using linear optics. Here we propose a simple experimental scheme by utilizing the dispersive interaction in superconducting quantum circuit to implement a hybrid Fredkin gate with a superconducting flux qubit as the control qubit and two separated quantum memories as the target qudits. The quantum memories considered here are prepared by the superconducting coplanar waveguide resonators or nitrogen-vacancy center ensembles. In particular, it is shown that this Fredkin gate can be realized using a single-step operation and more importantly, each target qudit can be in an arbitrary state with arbitrary degrees of freedom. Furthermore, we show that this experimental scheme has many potential applications in quantum computation and quantum information processing such as generating arbitrary entangled states (discrete-variable states or continuous-variable states) of the two memories, measuring the fidelity and the entanglement between the two memories. With state-of-the-art circuit QED technology, the numerical simulation is performed to demonstrate that two-memory NOON states, entangled coherent states, and entangled cat states can be efficiently synthesized.
We propose the generation of effective three-body interactions in superconducting circuits by coupling qubits or resonators to a bus qubit. Such interactions are characterized by energy exchange between two qubits or resonators depending on the state of the bus qubit. We show that a controlled-iswap (-iswap\sqrt{\mathrm{i}swap}iswap​) gate can be naturally implemented based on the three-body interactions and it can be used to construct a quantum Fredkin (controlled-swap) gate. A generalized Fredkin gate which controls the swapping of photons between two resonators can be realized in a similar way. It can be used to generate the entangled state of a high number of photons. This proposal is promising to be demonstrated with superconducting circuits previously reported and will stimulate the implementation of multiqubit quantum gates based on many-body interactions.
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.