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arXiv:1610.00232 · Physical Review A

Experimental generation of a high-fidelity four-photon linear cluster state

Chao Zhang, Yun‐Feng Huang, Bi‐Heng Liu, Chuan‐Feng Li, Guang‐Can Guo

Published Jun 22, 2016• 19 citations
arXivHTMLPDF

Abstract

Cluster state plays a crucial role in one-way quantum computation. Here, we propose and experimentally demonstrate a scheme to prepare an ultrahigh-fidelity four-photon linear cluster state via a spontaneous parametric down-conversion process. The state fidelity is measured to be $0.9517\ifmmode\pm\else\textpm\fi{}0.0027$. Our scheme can be directly extended to more photons to generate an $N$-qubit linear cluster state. Furthermore, our scheme is optimal for generating photonic linear cluster states in the sense of achieving the maximal success probability and having the simplest strategy. The key idea is that the photon pairs are prepared in some special nonmaximally entangled states instead of the normal Bell states. To generate a $2N$-qubit linear cluster state from $N$ pairs of entangled photons, only $(N\ensuremath{-}1)$ Hong-Ou-Mandel interferences are needed and a success probability of ${(\frac{1}{4})}^{N\ensuremath{-}1}$ is achieved.

DOI
10.1103/physreva.93.062329

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We report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon-photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups which are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability of each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to 1/2^(n-1); m-tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of 1/4^(m-1).
Abstract We report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon–photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to an m -tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of (1/4) m −1 .
We propose a scheme to generate a four-photon polarization-entangled cluster state by using only linear optical elements and four-photon coincidence detection. The scheme requires two single-photon states and one two-photon polarization entangled state as input resources. Then, we consider the realistic implementation of the scheme by using the spontaneous parametric down-conversion as photon resources. It is shown that under certain conditions, the four-photon polarization cluster state can be generated with a high fidelity, and the scheme is feasible by current experimental technology.
A scheme is proposed for generating a polarization four-photon cluster, which is believed to be suitable to achieve the one-way quantum computing via single-qubit projective measurements, with the help of only cross-Kerr nonlinearity and current linear optical systems. Compared with the existing schemes, the distinct advantage of the present scheme is that cluster states can be achieved with high success probability close to unity. Our scheme is experimentally demanding but efficient. Based on the present scheme, the cluster state of 3N + 1 photons can be obtained with the help of linear optical elements.
We experimentally demonstrate a simple scheme for generating a four-photon entangled cluster state with fidelity over 0.860+/-0.015. We show that the fidelity is high enough to guarantee that the produced state is distinguished from Greenberger-Horne-Zeilinger, W, and Dicke types of genuine four-qubit entanglement. We also demonstrate basic operations of one-way quantum computing using the produced state and show that the output state fidelities surpass classical bounds, which indicates that the entanglement in the produced state essentially contributes to the quantum operation.