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Scientific Reports

A heralded and error-rejecting three-photon hyper-parallel quantum gate through cavity-assisted interactions

Jizhen Liu, Hai‐Rui Wei, Ning‐Yang Chen

Published Jan 24, 2018• 12 citations
Publisher

Abstract

Hyper-parallel quantum computation is a promising and fruitful area of research with its high capacity and low loss rate characters. In this paper, we propose a heralded, compact, scalable, and deterministic error-rejecting scheme for implementing three-photon hyper-parallel Toffoli gate simultaneously acting on polarization and spatial degrees of freedom. It is a practical and unity gate without strong coupling strength limitations, since the undesired performances caused by the side leakage and the limited coupling strength are detected by the single-photon detectors. The success of our proposal can be heralded by the detectors, and the efficiency can be further improved by repeating the operation processes when the detectors are clicked. The evaluation of gate performance with experimental parameters shows that it is feasible with current experimental technology.

DOI
10.1038/s41598-018-20148-z

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Hyper-parallel quantum computation is a promising and fruitful area of research with its high capacity and low loss rate characters. In this paper, we propose a heralded, compact, scalable, and deterministic error-rejecting scheme for implementing three-photon hyper-parallel Toffoli gate simultaneously acting on polarization and spatial degrees of freedom. It is a practical and unity gate without strong coupling strength limitations, since the undesired performances caused by the side leakage and the limited coupling strength are detected by the single-photon detectors. The success of our proposal can be heralded by the detectors, and the efficiency can be further improved by repeating the operation processes when the detectors are clicked. The evaluation of gate performance with experimental parameters shows that it is feasible with current experimental technology.
We present an error-detected hyperparallel Toffoli (hyper-Toffoli) gate for a three-photon system based on the interface between polarized photon and cavity-nitrogen-vacancy (NV) center system. This hyper-Toffoli gate can be used to perform double Toffoli gate operations simultaneously on both the polarization and spatial-mode degrees of freedom (DoFs) of a three-photon system with a low decoherence, shorten operation time, and less quantum resources required, in compared with those on two independent three-photon systems in one DoF only. As the imperfect cavity-NV-center interactions are transformed into the detectable failures rather than infidelity based on the heralding mechanism of detectors, a near-unit fidelity of the quantum hyper-Toffoli gate can be implemented. By recycling the procedures, the efficiency of our protocol for the hyper-Toffoli gate is improved further. Meanwhile, the evaluation of gate performance with achieved experiment parameters shows that it is feasible with current experimental technology and provides a promising building block for quantum compute.
Photonic hyper-parallel quantum information processing (QIP) can simplify the quantum circuit and improve the information-processing speed, as well as reduce the quantum resource consumption and suppress the photonic dissipation noise. Here, utilizing the singly charged semiconductor quantum dot (QD) inside single-sided optical microcavity as the potentially experimental platform, we propose five schemes for heralded four-qubit hyper-controlled-not (hyper-CNOT) gates, covering all cases of four-qubit hyper-CNOT gates operated on both the polarization and spatial-mode degrees of freedom (DoFs) of a two-photon system. The novel heralding mechanism improves the fidelity of each hyper-CNOT gate to unity in principle without the strict restriction of strong coupling. The adaptability and scalability of the schemes make the hyper-CNOT gates more accessible under current experimental technologies. These heralded high-fidelity photonic hyper-CNOT gates can therefore have immense utilization potentials in high-capacity quantum communication and fast quantum computing, which are of far-reaching significance for QIP.
Quantum computing in high-dimensional spaces holds promise for a plethora of applications, i.e., handling more intricate information and executing wider quantum operations, in complex quantum information technologies (QITs). In the paper, we set up an error-heralded, resource-saving, circuit-simplified, and 4×4-dimensional controlled-not (CNOT) gate, where the polarized and spatial state of the flying photon (i.e., the control qudit) can effectively control the collective spin wave state of two atomic ensembles (i.e., the target qudit) in two double-sided cavities. Moreover, through meticulous analysis, the feasibility of the high-dimensional gate using existing technology boasts the exceptional performance including a near-unity fidelity and high efficiency exceeding 0.95, in principle, as the undesired performances originated from the little side leakage and the finite coupling strength, and the imperfect atom-ensemble-cavity interactions are heralded by single-photon detectors. Besides, auxiliary photons or atomic ensembles are unnecessary. Therefore, our protocol stands out for its simplicity, efficient resource utilization, and real-time error prediction, contributing significantly to the efficacy of QIT and charting a promising path towards the realization of high-dimensional quantum computing endowed with heightened capabilities.
Hyperparallel quantum information processing outperforms its traditional parallel one in terms of channel capacity, low loss rate, and processing speed. We present a way for implementing a robust hyperparallel optical controlled-phase-flip gate through microcavities. The gate acts on polarization and spatial degrees of freedom simultaneously, and the incomplete and undesired interactions between photons and quantum dots are prevented. Interestingly, the unity-fidelity of the gate can be achieved in principle, and the success of the gate is heralded by the single-photon detectors.
Implementing three-qubit Toffoli gates nonlocally plays an important role in quantum communication networks and distributed quantum computation. Most of previous protocols for implementing quantum Toffolis gate consider only implementing Toffoli gates with one degree of freedom. In this paper, we present a scheme for parallel implementation of nonlocal Toffoli gates in polarization and spatial-mode degrees of freedom assisted by quantum dots inside a double-side optical microcavity. Alice and Bob let photons traverse the double-side optical microcavity sequentially and perform single-particle measurements on electron spin in quantum dots and the entangled photons. Charlie performs single-particle measurements and applies the corresponding unitary operation in polarization and spatial-mode degrees of freedom according to Alice and Bob’s measurement results. Alice and Bob can implement hyper-parallel nonlocal Toffoli gates by performing unitary operations according to Charlie’s measurement result. This protocol has the advantage of having high channel capacity by the hyperentangled state as the quantum channel.
It is well known that a parallel quantum computer is more powerful than a classical one. So far, there are some important works about the construction of universal quantum logic gates, the key elements in quantum computation. However, they are focused on operating on one degree of freedom (DOF) of quantum systems. Here, we investigate the possibility of achieving scalable hyper-parallel quantum computation based on two DOFs of photon systems. We construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating on both the spatial-mode and the polarization DOFs of a two-photon system simultaneously, by exploiting the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics (QED). This hyper-CNOT gate is implemented by manipulating the four qubits in the two DOFs of a two-photon system without auxiliary spatial modes or polarization modes. It reduces the operation time and the resources consumed in quantum information processing, and it is more robust against the photonic dissipation noise, compared with the integration of several cascaded CNOT gates in one DOF.