基于连续变量多模纠缠态的量子拓扑特性研究

Multi-partite quantum entangled state is an important resource for quantum computation and quantum communication. The multi-partite entangled state can be used to show the topological properties of the anyons. The properties can be used in the topological quantum computation and can realize quantum computation with high fault-tolerant thresholds. Based on the continuous variable quantum information theory and the quantum optics experimental technologies, this project starts from the point of efficient preparation of continuous variable entangled states and its application in demonstrating of the statistical properties of the anyons. Based on the 6-8 modes entangled states corresponding to the topological code, the aim of this project is to explore the suitable experimental scheme. This project uses the fact that the continuous variable quantum progress can be realized deterministically and the potential association between the multi-partite entangled states and the topological code to explore an efficient preparation scheme for the required topological code. What’s more, we will research the recognition of the anyons, the robustness of the topological code for displacement errors, the topological properties of processes such as fusing and braiding, the properties in the process of continuous variable topological error correction and so on. The project applicant has the theoretical and experimental background of the related aspects such as quantum entanglement, one-way quantum computation and quantum error correction in continuous variables. This project may provide references for topological quantum computation and quantum error correction.

多模量子纠缠态是实现量子计算、量子通信等过程的重要资源。利用多模纠缠态可以演示任意子的拓扑特性，该特性可以用于拓扑量子计算过程，可以实现高容错阈值的量子计算方式。本项目以连续变量量子信息理论和量子光学实验技术为基础，从连续变量纠缠资源的高效制备及其在验证任意子分数统计特性方面的应用出发，围绕6-8组份纠缠态研究所对应的拓扑编码结构，探索相关的实验实现方案。本项目结合连续变量量子过程确定性实现的特色，利用多模纠缠态与拓扑编码结构之间的潜在关联，探索所需编码结构的高效精简制备方案，并基于此研究任意子类型的判断、拓扑编码结构对平移误差的抗干扰规律、任意子间合并交织等过程的拓扑特性、连续变量拓扑纠错过程的特性等内容。项目的申请者具有连续变量量子纠缠、单向量子计算、量子误差修正等相关方面的理论与实验技术基础，该项目的研究可为拓扑量子计算、量子纠错等相关实验工作提供参考。

拓扑误差修正是一种能提供校正量子计算误差的有效方法。它使量子计算能够以更高的容错阈值和损耗容忍度得以实现。我们提出了一种基于连续变量八组份的高斯纠缠簇态的拓扑误差纠正方案。该方案提供了一种可行的连续变量拓扑误差修正方案，方案可以用高斯纠缠cluster态通过实验证明。除了量子纠缠和导引外，量子相干性也被认为是量子信息中的一种有用的量子资源。它是一种非常重要的研究实际的量子通道中量子相干特性演化的过程。我们通过实验分别量化了压缩态和EPR纠缠态在高斯热噪声通道中传输的量子相干特性。通过重构输出态的协方差矩阵，这些高斯态的量子相干性通过计算相对熵来量化。我们证明了压缩态和高斯EPR纠缠态的量子相干性对量子通道中的损耗和噪声具有鲁棒性。我们基于拓扑纠缠态结构的连续变量光场模式下任意子类型的判断、拓扑编码对误差的抗干扰规律、任意子间的合并交织等拓扑特性的研究工作，设计了四组份拓扑编码结构以及其实现任意子交织特性的实验方案。我们还研究了连续变量量子信息过程中相位控制技术的两种具体技术，一种可以精简相位锁定系统，一种可以方便的稳定相对相位，为量子传感测量提供帮助。

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