多端约瑟夫森效应的理论研究及其在量子计算中的应用

随着新材料和纳米科学的快速发展，多端约瑟夫森效应近年来在介观物理学界受到广泛关注。相较于传统的二端约瑟夫森结，多端约瑟夫森结具有更多引人入胜的性质，进而能为量子计算的发展提供更广阔的平台。多端结中的安德列夫束缚态可以模拟拓扑能带。多端结具有复杂的量子动力学及非线性响应特性。基于二维电子气的平面多端结可能实现马约拉纳模的辫子操作。此外，多端结也可用于高保真度高集成度多量子比特门的设计。然而，多端约瑟夫森结的一般理论及其在量子器件中的应用仍有待进一步探索。在本项目中，我们将在多体物理的框架下对多端约瑟夫森结的动力学性质进行系统的理论研究，并讨论其在量子计算中的潜在应用。在动力学性质方面，我们将重点研究拓扑安德列夫能带的输运特性、相位场耗散相变、相位场—马约拉纳模耦合动力学等问题。在器件应用方面，我们将从多端结有效哈密顿量模型出发，分析多量子比特门实现的可行性，进而给出模型的最优参数。

Along with the fast developing material science and nanotechnology, the multiterminal Josephson effects have recently become one of the focuses of the mesoscopic physics. Compared to the conventional two-terminal Josephson junctions, the multiterminal Josephson junctions exhibit more fascinating properties and offer a broader platform for the quantum computation. The Andreev subgap states of the multiterminal Josephson junctions can simulate topological bands. The multiterminal junctions exhibit complex quantum dynamics and nonlinear response properties. The multiterminal planar junctions based on two-dimensional electron gases provide a potential platform for Majorana modes braiding. In addition, the multiterminal junctions can be exploited to design high-fidelity and high-density multiqubit gates. Nevertheless, the general theory of the multiterminal Josephson effects and its application to the quantum devices remain to be explored. In this project, we will carry out a comprehensive theoretical study on the quantum dynamics of the multiterminal Josephson junctions in the framework of many-body physics, and discuss its potential applications to the quantum computation. We will focus on the dynamical problems such as the transport signatures of the topological Andreev bands, the dissipative phase transition of phase fields, and the dynamics of coupled phase fields and Majorana modes. On the other hand, in the aspect of the quantum devices, we will analyze the feasibility of applying multiterminal junctions to multiqubit gates via the effective Hamiltonian approach and obtain the optimized model parameters.