中文摘要：

拓扑相是一类不能由经典朗道对称破缺理论描述的奇特物质态.这种态具有一些有趣的性质,如依赖于拓扑流形的基态简并度、准粒子分数统计和拓扑纠缠熵等.拓扑相的性质研究在凝聚态物理中本身具有重要意义,如促进新型材料的发现.另一方面,拓扑相提供了一种天然的无噪声介质,在容错量子计算领域也有着潜在的应用.然而,受限于当前苛刻的实验条件和可控的实验手段,在真实体系中观测并探索拓扑相的性质是一件困难的事情.量子模拟用一个可控的量子系统模拟复杂的或难以观测的物理现象,为我们研究拓扑相提供了有力手段.核磁共振体系作为量子模拟的物理实现平台之一,在多量子比特实验中具有成熟的控制技术和精确的测量手段,是一个很好的测试平台.本文首先介绍拓扑相的基本概念和性质,回顾核磁共振在量子模拟中的应用,然后讨论基于该体系完成的关于拓扑相量子模拟的几个实验工作,最后给出总结并展望此研究领域的前景.

英文摘要：

Topological phases are exotic states of quantum matter which are beyond the usual symmetry description.These phases have some interesting properties,such as robust ground state degeneracy that depends on the surface topology,quasiparticle fractional statistics,topological entanglement entropy,etc. Topological phases not only play a significant role in the basic scientific research of condensed matter physics,but also provide a natural medium for fault-tolerant quantum computation. Quantum simulation suggests that the complicated or inaccessible physical phenomena can be simulated by a controlled quantum system,which will provide a powerful means to explore topological phases and their topological properties. Nuclear magnetic resonance,as one physical implementation of quantum simulation,is a good test platform due to its sophisticated control and precise measurement in multi-qubit experiments. In this paper,topological phases and nuclear magnetic resonance quantum simulator are reviewed,and three related experiments on quantum simulation of topological phases are introcluced. Finally,a summary and an outlook towards topological quantum computation are given.