我们数值研究了二维拓扑超导体中涡旋的非阿贝尔编织动力学，例如具有Rashba自旋轨道耦合的$s$波超导体。由涡旋承载的马约拉纳零模（MZM）构成拓扑量子比特，这提供了拓扑量子计算的基本构建块。然而，由于MZM受到$\mathbb{Z}_2$不变量的保护，所以马约拉纳量子比特和量子门操作可能对由准粒子干涉引起的本征退相干敏感。在不假设${\it a \ priori}$存在MZM的情况下，数值模拟了含时Bogoliubov-de Gennes方程，研究了非阿贝尔辫状动力学中由于与邻近MZM和其他准粒子态相互作用而引起的幺正算符上的量子噪声.我们表明，交换后的两个涡，最低的涡束缚态积累的几何相位$π/2$，和来自动力学相位的误差是可以忽略不计的小，无论MZM的相互作用。此外，我们还数值模拟了二维拓扑超导体中四个涡旋的编织动力学，讨论了一个最佳编织条件，以实现基于Majorana的量子比特的高性能非阿贝尔统计和量子门操作.
英文摘要：
We numerically investigate non-Abelian braiding dynamics of vortices in two-dimensional topological superconductors, such as $s$-wave superconductors with Rashba spin-orbit coupling. Majorana zero modes (MZMs) hosted by the vortices constitute a topological qubit, which offers a fundamental building block of topological quantum computation. As the MZMs are protected by $\mathbb{Z}_2$ invariant, however, the Majorana qubit and quantum gate operations may be sensitive to intrinsic decoherence caused by quasiparticle interference. Numerically simulating the time-dependent Bogoliubov-de Gennes equation without assuming ${\it a \ priori}$ existence of MZMs, we examine quantum noises on the unitary operators of non-abelian braiding dynamics due to interactions with neighboring MZMs and other quasiparticle states. We demonstrate that after the interchange of two vortices, the lowest vortex-bound states accumulate the geometric phase $π/2$, and errors stemming from dynamical phases are negligibly small, irrespective of interactions of MZMs. Furthermore, we numerically simulate the braiding dynamics of four vortices in two-dimensional topological superconductors, and discuss an optimal braiding condition for realizing the high performance of non-Abelian statistics and quantum gates operations of Majorana-based qubits.
Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortex matter in a ${p_x}+i{p_y}$ superconductor
$1/3$-Flux Bound States in Multicomponent Superconductor Exhibiting Non-Abelian Statistics of $\mathbb {Z}_3$ Parafermions
Interdisciplinary Center for Theoretical Physics and Information Sciences, Fudan University（复旦大学理论物理与信息科学交叉中心）；State Key Laboratory of Surface Physics and Department of Physics, Fudan University（复旦大学表面物理国家重点实验室和物理系）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Hefei National Laboratory（合肥国家实验室）
