超导电路中开放连续变量系统介观拓扑性质研究

The topological states of matter can be characterized by topological invariant-the Chern number, whose robustness against disorder has made topological systems important tools for quantum science and technology. However, the global topological properties are typically destroyed by dissipation. In order to use the global topological protection properties, one method is to isolate the topological systems from the environment and then to make coherent control; another method is to engineer the dissipation-protection mechanisms for the system-environment coupling. The two cases can respectively facilitate the system's nonadiabatic response that deviates the eigenstates and steady states evolution. The project is based on the superconducting circuit systems, aims to study the dissipation as the positive factor for driving the steady states, as to explore the topological properties of the continuous variable systems; As the steady states induced by the involved dissipative dynamics are mesoscopic superposition or entanglement of continuous variables, the system’s evolution that deviates from the adiabatic trajectory will cause mesoscopic topological properties that are closest to the classical cases, which cannot be achieved by the recent theories and experiments that use discrete systems; Moreover, the steady states induced by the dissipative dynamics are the specific superposition or entanglement of cat states that possess odd-even parity, the single photon decay that could cause the steady states dephasing will only induce the cat states with different parity to interchange, but not influence the form of the steady states, which will make the nonadiabatic responses to get the Berry curvature insensitive to the fluctuation of environment, relaxing the requirement for the physical demonstration.

物质的拓扑态可由拓扑不变量-陈数来刻画，它们对无序的鲁棒性使拓扑系统有望成为量子科学与技术的重要工具。但是，全局的拓扑特性通常会被耗散所破坏。为了利用拓扑系统的全局拓扑保护特性，一是可以把拓扑系统与环境隔绝并进行相干控制，二是可以构建系统与环境耦合的耗散保护机制，两种情形可分别促成系统作背离本征态演化和稳态演化的非绝热响应。本课题基于超导电路系统，研究耗散作为驱动稳态的积极因素，探索开放连续变量系统中的介观拓扑性质；由于所涉及的耗散动力学所诱导的稳态是连续变量介观叠加或纠缠，系统背离绝热轨迹的演化将导致最接近于经典的介观拓扑特性，这在当前使用分离变量系统的理论和实验中尚不能实现；此外，耗散动力学所诱导的稳态，是具有奇偶宇称的猫态的特定叠加或纠缠，引起稳态失相的单光子衰竭将只会导致不同宇称的猫态互换，不影响稳态形式，这将使获取贝里曲率的非绝热响应对环境的起伏不敏感，放宽了对物理实施的要求。

量子信息可分别以两种方式来呈现，一是分离变量，如自旋-1 /2系统，可以自然地充当一个比特；二是连续变量，比如奇偶猫态，也可作为比特的两个基矢。探索和挖掘两种编码方式的优势并应用于量子信息处理以及拓扑物态研究已经成为当今量子领域研究的重要课题。本项目综合利用两种编码方式，主要完成了如下实验和理论研究成果。. 提出并在超导电路系统中实现了连续变量准正交相干态编码的两个微波光场间的控制相位门；并进一步实现了具有纠错功能的两二项式编码逻辑比特间的控制相位门。. 提出并在超导电路系统中实现了混杂连续变量-分离变量五体GHZ最大纠缠态，验证了五体贝尔不等式。. 提出了在超导电路开放量子网路系统中实施多比特初始化的新方法。该方法不依赖于比特的数目且对系统参量的大范围起伏不敏感，也可进一步推广应用到高维量子网络系统中。. 提出了利用受驱动超导比特的哈密顿量参量流形来构造两类拓扑结构：球面和环面，研究表明比特系统的态演化可以通过对贝里曲率的获取来跟踪和被操控。. 首次在超导电路系统中展示了高保真度的确定性量子纠缠交换实验，并进一步演示了延迟选择的纠缠交换实验，结果表明两个量子比特在先前表现出纠缠行为还是可分行为取决于事后对它们合作比特的测量选择。. 首次在超导电路系统中展示了高保真度的普适量子克隆机。量子不可克隆定理禁止未知量子态的完美克隆。普适量子克隆机能够以最佳保真度产生一个任意比特的两份近似拷贝，具有重要的理论意义，并且在量子信息处理方面具有重要应用。我们在一个超导电路中实现了普适量子克隆机，并且首次定量刻画了输入比特与拷贝比特之间的非经典关联这一普适行为。. 在超导电路系统中率先实现了基于和乐变换的两比特受控非门。和乐变换具有对噪声不敏感的特性，而超导电路被认为是最有希望实现可扩展量子计算的系统。因此，如何在该系统中实现通用的和乐量子逻辑门对量子计算的实现具有重要意义，但以往基于该系统所报道的和乐门只限于单比特，我们的方法使得和乐量子计算的研究往前迈进了重要一步。. 提出并在超导电路系统中演示了开放系统动力学控制方法，该方法其中一个重要应用是稳定量子电池的能量。