Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Special Issue: The 4th Young Scientist Meeting on Statistical Physics and Information Processing in Sendai
Quantum Information and Statistical Mechanics: An Introduction to Frontier
Keisuke FUJII
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2013 Volume 19 Issue 1 Pages 1-15

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Abstract

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.

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© 2013 by the Graduate School of Information Sciences (GSIS), Tohoku University
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