Introduction to topological quantum computation with non-Abelian anyons
Introduction to topological quantum computation with non-Abelian anyons
复制标题
DOI：
10.1088/2058-9565/aacad2
复制
发表时间：
2018-10-01
影响因子：
6.7
通讯作者：
Simula, Tapio
中科院分区：
文献类型：
--
作者：
Field, Bernard;Simula, Tapio
拓扑量子计算机为量子计算提供了一种容错手段。拓扑量子计算机使用具有奇异交换统计的粒子，称为非阿贝尔任意子，而允许通过粒子交换或单独编织进行普遍量子计算的最简单的任意子模型是斐波纳契任意子模型。利用量子计算可以有效解决的一个经典难题是求单位根处的纽结的琼斯多项式的值。我们的目标是用斐波那契任意子对拓扑量子计算提供一个完整的教学回顾，从编织统计和矩阵到这样的计算机的布局和编织以执行特定的操作。然后，我们使用一个拓扑量子计算机的模拟来显式地演示使用斐波那契任意子的量子计算，计算一组简单纽结的琼斯多项式。除了模拟模块化电路风格的量子算法外，我们还展示了如何使用斐波那契或伊辛任意子精确地获得特定点上琼斯多项式的量级。这种精确的算法似乎非常适合于拓扑量子计算机的概念证明演示。
Topological quantum computers promise a fault tolerant means to perform quantum computation. Topological quantum computers use particles with exotic exchange statistics called non-Abelian anyons, and the simplest anyon model which allows for universal quantum computation by particle exchange or braiding alone is the Fibonacci anyon model. One classically hard problem that can be solved efficiently using quantum computation is finding the value of the Jones polynomial of knots at roots of unity. We aim to provide a pedagogical, self-contained, review of topological quantum computation with Fibonacci anyons, from the braiding statistics and matrices to the layout of such a computer and the compiling of braids to perform specific operations. Then we use a simulation of a topological quantum computer to explicitly demonstrate a quantum computation using Fibonacci anyons, evaluating the Jones polynomial of a selection of simple knots. In addition to simulating a modular circuit-style quantum algorithm, we also show how the magnitude of the Jones polynomial at specific points could be obtained exactly using Fibonacci or Ising anyons. Such an exact algorithm seems ideally suited for a proof of concept demonstration of a topological quantum computer.