---
title: Introduction
description: A free IBM course on quantum information and computation
source: https://quantum.cloud.ibm.com/learning/en/courses/foundations-of-quantum-error-correction/stabilizer-formalism/introduction
---

# Introduction

In the previous lesson, we took a first look at quantum error correction, focusing specifically on the 9-qubit Shor code.
In this lesson, we'll introduce the *stabilizer formalism*, which is a mathematical framework through which a broad class of quantum error correcting codes, known as *stabilizer codes*, can be specified and analyzed.
This includes the 9-qubit Shor code along with many other examples, including codes that seem likely to be well-suited to real-world quantum devices.
Not every quantum error correcting code is a stabilizer code, but many are, including every example that we'll see in this course.

The lesson begins with a short discussion of Pauli matrices, and tensor products of Pauli matrices more generally, which can represent not only operations on qubits, but also measurements of qubits — in which case they're typically referred to as *observables*.
We'll then go back and take a second look at the repetition code and see how it can be described in terms of Pauli matrix observables.
This will both inform and lead into a general discussion of stabilizer codes, including several examples, basic properties of stabilizer codes, and how the fundamental tasks of encoding, detecting errors, and correcting those errors can be performed.

## Lesson video

In the following video, John Watrous steps you through the content in this lesson on stabilizer formalism. Alternatively, you can open the [YouTube video](https://youtu.be/3ib2JP_LeIU?list=PLOFEBzvs-VvqKKMXX4vbi4EB1uaErFMSO) for this lesson in a separate window. [Download the slides](https://ibm.box.com/public/static/umposbds8d27cv8rnpsayyaj1k2aw88o.pdf) for this lesson.