Stabilizer Codes and Quantum Error Correction

TL;DR

This paper provides an overview of quantum error correction focusing on stabilizer codes, their structure, known codes, and implications for quantum communication and fault-tolerance.

Contribution

It introduces the formalism of stabilizer codes and discusses their applications, bounds, and role in fault-tolerant quantum computation.

Findings

Stabilizer codes offer a structured approach to quantum error correction.

Quantum channel capacity and bounds on quantum codes are analyzed.

Stabilizer codes are fundamental for fault-tolerant quantum computation.

Abstract

Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed to meet this challenge. A group-theoretical structure and associated subclass of quantum codes, the stabilizer codes, has proved particularly fruitful in producing codes and in understanding the structure of both specific codes and classes of codes. I will give an overview of the field of quantum error correction and the formalism of stabilizer codes. In the context of stabilizer codes, I will discuss a number of known codes, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation.