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Basics of quantum information
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This is the first unit of the Understanding Quantum Information and Computation series, which explains quantum information and computation at a detailed mathematical level.

The first unit, Basics of Quantum Information, begins with a mathematical description of quantum information for both single and multiple systems, then moves on to quantum circuits, and finally covers three fundamentally important examples — quantum teleportation, superdense coding, and the CHSH game — all of which are connected to the phenomenon of entanglement.

The series includes both written content and videos featuring John Watrous.

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Lessons

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Single systems
  • Introduction
  • Classical information
  • Quantum information
  • Qiskit examples
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Multiple systems
  • Introduction
  • Classical information
  • Quantum information
  • Qiskit examples
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Quantum circuits
  • Introduction
  • Circuits
  • Inner products, orthonormality, and projections
  • Limitations on quantum information
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Entanglement in action
  • Introduction
  • Teleportation
  • Superdense coding
  • The CHSH game
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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

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

  • Khan Academy: Linear algebra

    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. In the video How to install Qiskit, Nick Brønn helps you get Qiskit running.

Credly

IBM leverages the services of Credly, a 3rd party data processor authorized by IBM and located in the United States, to assist in the administration of the IBM Digital Badge program. In order to issue you an IBM Digital Badge, your personal information (name, email address, and badge earned) will be shared with Credly.

You will receive an email notification from Credly with instructions for claiming the badge. Your personal information is used to issue your badge and for program reporting and operational purposes. IBM may share the personal information collected with IBM subsidiaries and third parties globally. It will be handled in a manner consistent with IBM Privacy Statement.