An Introduction to Error-Correcting Codes: From Classical to Quantum

TL;DR

This paper provides an overview of quantum error-correcting codes, highlighting their similarities to classical codes and discussing the unique challenges posed by quantum channels in developing robust quantum error correction methods.

Contribution

It surveys the current state of quantum error correction, emphasizing the lessons learned from classical coding theory to advance quantum code development.

Findings

Quantum error correction shares many concepts with classical coding.

Quantum channels behave differently, posing unique challenges.

Classical error control methods can inform quantum code development.

Abstract

This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in developing robust quantum codes. Fortunately, the classical error control methods have been well developed. If we can learn many lessons from classical coding theory, we can expedite the development of quantum codes. Scientists have discovered that quantum error correction shares many concepts with classical counterpart. Both quantum and classical coding schemes add redundancy to information to protect against noises. They also have similar conditions for error detectability and correctability.