Quantum information and statistical mechanics: an introduction to frontier

TL;DR

This paper reviews the intersection of quantum information science and statistical mechanics, focusing on stabilizer formalism, quantum error correction, and algorithms for classical spin models.

Contribution

It introduces the stabilizer formalism and explores its applications in quantum error correction and evaluating classical spin model partition functions.

Findings

Stabilizer formalism efficiently describes stabilizer states and operations.

Quantum error correction codes relate to spin glass models for performance analysis.

Partition functions of classical spin models can be evaluated using quantum algorithms.

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.