基于斐波那契任意子的拓扑序模拟及其测量

SIMULATION AND MEASURENMENT OF TOPOLOGICAL ORDER BASED ON FIBONACCI ANYON

庹晨

11849415

硕士

物理学

吴健生

2020-05-29

2020-07-14

哈尔滨工业大学

深圳

近些年来拓扑这一数学概念在物理学界吸引了大家的广泛关注，与此同时 基于量子力学原理而构建的量子计算机近期的发展也十分迅速。量子计算机由 于其具有远远超出普通经典计算机计算能力的特点受到了人们的追捧，然而退 相干和噪声是实现通用量子计算机的两个主要障碍。为了打破这一瓶颈，一方 面量子纠错被提出，而另一方面拓扑量子计算这一应对策略也被提出。由于系 统的整体拓扑性质，拓扑量子计算具有天然的免疫噪声能力。因此拓扑量子计 算也是目前容错率最高的量子计算方案。 而拓扑序是一种超越朗道对称破缺范式的新型物质相，在拓扑量子计算中 有潜在的应用前景。在真实物理系统中观测拓扑序极具挑战，而量子模拟器作 为一种特殊用途的量子计算装置提供了一种表征拓扑序的方法。一般认为，拓 扑序可以由 F-矩阵和 R-矩阵来进行完整的描述。其中 R-矩阵已被证实是可以 被直接实验测得的，然而 F-矩阵是否是可以被直接测得还未知。F-矩阵和 R- 矩阵如果都能够被实验直接测得，那么我们说拓扑序是可以直接被测得的。本 文展示了如何通过数字式量子模拟器对弦网模型描述的双斐波那契序进行模拟 并测量其 F-矩阵，与此同时也完成了该模型上三种拓扑序的识别。在 F-矩阵得 到有效模拟的基础上我们可以进一步模拟编织操作，并最终通过编织进行拓扑 量子计算。

In recent years, the mathematical concept of topology has attracted wide attention in the field of physics, while the quantum computer based on the principles of quantum mechanics has developed rapidly in the near future. Quantum computation are popular because of the strong computing power, which is far beyond the ordinary classical computers. However, decoherence and noise are two main obstacles to the realization of universal quantum computers. In order to break this bottleneck. On the one hand, quantum error correction is proposed. On the other hand, topological quantum computation is also proposed as a coping strategy. Because of the whole topological property of the system, topological quantum computation has natural capability which can immune environment noise. So topological quantum computation is also regarded as one efficient way to realize quantum computation and has maximum tolerance. The topological order is a new kind of phase of the matter which surpasses the Landau symmetry breaking paradigm and has potential application in topological quantum computation. Observing topological order is extremely challenging in real physical systems, but quantum simulator as a special purpose quantum computing device provides a way to characterize topological order. It is generally believed that the topological order can be fully described by F-matrix and R-matrix, where the R-matrix has been confirmed to be directly experimentally measured, however whether the F-matrix can be directly measured is unknown. If F-matrix and R-matrix can be directly measured by experiments, then we say that the topological order can be directly measured. In this paper, we show how to use digital quantum simulator to simulate the doubled Fibonacci order which is described by the model of string net model and measure its F-matrix, at the same time, the recognition of three topological sequences on the model is completed. Based on the effective simulation of the F-matrix, we can further simulate the braiding operation and finally perform topological quantum computation through the braiding operation of anyons.

拓扑序 量子模拟 斐波那契任意子

topological order quantum simulation fbonacci anyon

中文

联合培养

南方科技大学

庹晨. 基于斐波那契任意子的拓扑序模拟及其测量[D]. 深圳. 哈尔滨工业大学,2020.