对非厄米拓扑物态的量子模拟

  量子信息及量子计算是一门基于量子力学的交叉学科，其目的是建造基于量子力学原理的、计算能力远超经典计算机的量子计算机。对于量子计算的研究，大概分为两大方向：量子算法和量子模拟。其中量子算法旨在利用量子力学中的相干性和叠加性为算法提供并行加速的运算能力；量子模拟则是利用可控量子系统去模拟目标量子系统的动力学。在具有量子计算潜力的物理体系中，核磁共振体系是研究最早也是目前发展最成熟的体系之一。虽然该体系的可拓展性存在问题，但是执行复杂精确的量子控制操作的能力使得它非常适合进行小规模的量子计算实验。本文的量子模拟实验就是基于核磁共振量子计算平台实现。

  量子拓扑物态的研究是凝聚态领域的一大热点。传统的量子拓扑相分类方法是基于平衡态定义的体拓扑不变量。这种表征在实验中具有挑战性，因为非局部拓扑不变量可能没有直接对应的可观测物理量。 最近，一种新的、在淬火动力学下定义的拓扑相理论被提出，这个理论为量子拓扑物态的实验研究带来了更好的可行性。而量子模拟就为这种基于淬火动力学的拓扑相研究提供了一个很好的平台：通过高可控性，量子模拟器可与拓扑系统建立映射关系，可在模拟器上模拟拓扑系统的动力学，并且可以直接在模拟器上测量拓扑不变量。

  目前尚没有非厄米的淬火动力学拓扑相的实验研究工作，但是噪声引起的非厄米效应在真实的量子系统中却又无处不在，并可能影响物质的基本状态。因此对非厄米的拓扑物态进行研究是非常有意义的。本论文的工作就是利用核磁共振平台对二维非厄米量子反常霍尔(QAH)模型进行量子模拟。与通常使用辅助量子比特引入非厄米效应的实验不同，本工作使用一种基于随机薛定谔方程的平均方法来引入非厄米耗散量子动力学，具有节省量子比特资源和简化量子门的优势。本实验工作证明了淬火动力学拓扑相在弱噪声下的稳定性，并观察到两种由强噪声驱动的拓扑相变以及一个对某些噪声总能保持拓扑性质稳定的特殊区域。该工作展示了一种可行的量子模拟方法，并为研究非厄米拓扑物理提供了另一个途径。 

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