Quantum information and statistical mechanics: an introduction to frontier
Quantum information and statistical mechanics: an introduction to frontier
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DOI：
10.4036/iis.2013.1
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发表时间：
2013-06
期刊：
影响因子：
--
通讯作者：
K. Fujii
中科院分区：
文献类型：
--
作者：
K. Fujii
本文是对量子信息科学和统计力学这一交叉学科领域的简要回顾。我们首先介绍了稳定器形式论，它是描述一类重要的量子态，即所谓的稳定器态，以及它们上的量子操作的一种有效方法。此外，还提到了与图相关的一类稳定子态--图态及其在基于测量的量子计算中的应用。基于稳定器形式主义，我们回顾了两个跨学科的主题。一个是量子纠错码与自旋玻璃模型之间的关系，它允许我们利用统计模型中的位相知识来分析量子纠错码的性能。二是经典自旋模型的稳定器形式与配分函数之间的关系，为计算经典自旋模型的配分函数提供了新的量子算法和经典算法。
This is a short review on an interdisciplinary field of quantum information science and statistical mechanics. We first give a pedagogical introduction to the stabilizer formalism, which is an efficient way to describe an important class of quantum states, the so-called stabilizer states, and quantum operations on them. Furthermore, graph states, which are a class of stabilizer states associated with graphs, and their applications for measurement-based quantum computation are also mentioned. Based on the stabilizer formalism, we review two interdisciplinary topics. One is the relation between quantum error correction codes and spin glass models, which allows us to analyze the performances of quantum error correction codes by using the knowledge about phases in statistical models. The other is the relation between the stabilizer formalism and partition functions of classical spin models, which provides new quantum and classical algorithms to evaluate partition functions of classical spin models.