Basics of Quantum Information 
Created by John Watrous
Welcome to Basics of Quantum Information, first course in the Understanding Quantum Information and Computation series comprising the following courses:
- Basics of quantum information
- Fundamentals of quantum algorithms
- General formulation of quantum information
- Foundations of quantum error correction (under construction)
This course begins with an introduction to the mathematics of quantum information, including a description of quantum information for both single and multiple systems. It then moves on to quantum circuits, which provide a standard way to describe quantum computations. Finally, three fundamentally important examples connected with the phenomenon of quantum entanglement are explained: quantum teleportation, superdense coding, and the CHSH game (also known as the CHSH inequality).
This course is intended for students, professionals, and hobbyists in fields such as computer science, physics, engineering, and mathematics who are eager to gain knowledge on the theoretical foundations of quantum information and computation.
Lessons
- Introduction
- Pre-course Survey
- Classical information
- Quantum information
- Qiskit implementations
- Introduction
- Classical information
- Quantum information
- Qiskit implementations
- Introduction
- Circuits
- Inner products, orthonormality, and projections
- Limitations on quantum information
- Introduction
- Teleportation
- Superdense coding
- The CHSH game
- Post-Course Survey
Exam
Take this exam to test your skills. This exam is intended to be taken after reading the lessons in this course. Once you have completed the exam, come back here to see your earned badge.
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Helpful materials
Learning goals
Upon completing the course, you will be able to:
- Recall linear algebra concepts used to describe classical and quantum states, measurements, and operations.
- Calculate quantum state descriptions after operations and measurements.
- Manipulate quantum state vectors using quantum circuits in Qiskit.
- Explain quantum entanglement to a friend or colleague and provide examples of its practical applications.
Recommended background
To make the most out of this course, we recommend familiarity with basic linear algebra, complex numbers, and elementary mathematical notions including sets and functions. The following sources are a few among many that cover this material
In this video series, Sal Khan introduces key concepts in linear algebra that we will rely upon.
Stephen Friedberg, Arnold Insel, and Lawrence Spence. Linear Algebra
This book on linear algebra covers the material we require, and also includes appendices on sets, functions, and complex numbers.
Sheldon Axler. Linear Algebra Done Right
A classic text on linear algebra suitable for those at or beyond an advanced undergraduate level.
Ricky Shadrach and Rod Pierce. Introduction to Sets
A beginner-level web page on sets that may help to bring some readers up to speed.
John K. Hunter. An Introduction to Real Analysis: Chapter 1
The first chapter of these lecture notes includes a more formal and detailed introduction to sets and functions.
Installing Qiskit
You don't need to install anything to start this course, but you may eventually want to write and run your own Qiskit programs. The Install Qiskit page explains how to get Qiskit running.
Presentation slides
Copies of the slides used to create the videos for this course are available for download in pdf format: