Li Keren, Wan Yidun, Hung Ling-Yan, Lan Tian, Long Guilu, Lu Dawei, Zeng Bei, Laflamme Raymond
State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.
Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada.
Phys Rev Lett. 2017 Feb 24;118(8):080502. doi: 10.1103/PhysRevLett.118.080502. Epub 2017 Feb 23.
Topological orders can be used as media for topological quantum computing-a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z_{2} toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.
拓扑序可作为拓扑量子计算的媒介，拓扑量子计算是一种很有前景的量子计算模型，因其对局部误差具有免疫能力。相反，量子模拟器通常被视为一种特殊用途的量子计算设备，它也提供了一种表征拓扑序的方法。在这里，我们展示了如何通过测量它们的模S和T矩阵来识别不同的拓扑序。特别地，我们利用核磁共振量子模拟器来研究由具有两种弦类型的弦网模型所描述的三个拓扑有序物质相的性质，包括Z₂ 环面码、双半子和双斐波那契。特别地，第三个，非阿贝尔斐波那契序被认为是通用拓扑量子计算的最简单候选者。我们的实验作为基本模块，在此基础上可以模拟非阿贝尔任意子的编织，并最终通过编织实现拓扑量子计算，从而提供了一种使用量子计算机研究拓扑序的新方法。
