Hai Yong-Ju, Zhang Ze, Zheng Hao, Kong Liang, Wu Jiansheng, Yu Dapeng
Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China.
Natl Sci Rev. 2022 Nov 24;10(3):nwac264. doi: 10.1093/nsr/nwac264. eCollection 2023 Mar.
Topological order is a new quantum phase that is beyond Landau's symmetry-breaking paradigm. Its defining features include robust degenerate ground states, long-range entanglement and anyons. It was known that and matrices, which characterize the fusion-braiding properties of anyons, can be used to uniquely identify topological order. In this article, we explore an essential question: how can the and matrices be experimentally measured? We show that the braidings, i.e. the matrices, can be completely determined by the half braidings of boundary excitations due to the boundary-bulk duality and the anyon condensation. The matrices can also be measured by comparing the quantum states involving the fusion of three anyons in two different orders. Thus we provide a model-independent experimental protocol to uniquely identify topological order. By using quantum simulations based on a toric code model with boundaries encoded in three- and four-qubit systems and state-of-the-art technology, we obtain the first experimental measurement of and matrices by means of an NMR quantum computer at room temperature.
拓扑序是一种超越朗道对称性破缺范式的新量子相。其定义特征包括稳健的简并基态、长程纠缠和任意子。已知用于表征任意子融合编织性质的(S)和(T)矩阵可用于唯一识别拓扑序。在本文中，我们探讨一个基本问题：如何通过实验测量(S)和(T)矩阵？我们表明，由于边界 - 体对偶性和任意子凝聚，编织，即(S)矩阵，可以由边界激发的半编织完全确定。(T)矩阵也可以通过比较涉及三个任意子以两种不同顺序融合的量子态来测量。因此，我们提供了一个与模型无关的实验方案来唯一识别拓扑序。通过使用基于具有编码在三量子比特和四量子比特系统中的边界的环面码模型的量子模拟以及最先进的技术，我们在室温下借助核磁共振量子计算机首次对(S)和(T)矩阵进行了实验测量。
