Topological Quantum Computation
Topological Quantum Computation
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DOI：
10.1007/978-3-642-38874-3_5
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发表时间：
2012-05
期刊：
影响因子：
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通讯作者：
J. Pachos
中科院分区：
文献类型：
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作者：
J. Pachos
拓扑量子计算的教学介绍包括以下部分。首先，我们介绍任意子和拓扑模型。我们特别考虑任意子的性质及其与拓扑量子计算的关系。然后我们提出量子双模型。这些是稳定器代码，可以非常类似于量子纠错码。它们包括环面码以及各种阿贝尔和非阿贝尔扩展。接下来提出琼斯多项式，它们是与任意子相关的链接和结的拓扑不变量。它们通过经典算法的评估在计算上是复杂的，但它们通过量子算法的近似是有效的。最后，我们概述了拓扑量子计算的现状，并提出了一些悬而未决的问题。
This pedagogical introduction to topological quantum computation includes the following parts. First we provide an introduction to anyons and topological models. In particular we consider the properties of anyons and their relation to topological quantum computation. Then we present the quantum double models. These are stabiliser codes, that can be described very much like quantum error correcting codes. They include the toric code and various Abelian and non-Abelian extensions. Next the Jones polynomials are presented, which are topological invariants of links and knots that are related to anyons. Their evaluations by classical algorithms is computationally complex, but their approximation by quantum algorithms is efficient. Finally, we presenter an overview of the current state of topological quantum computation and present some open questions.