Understanding Quantum Information and Computation (IBM Learning)

A complete graduate-level course on quantum information and computation, delivered as a four-part video lecture series by John Watrous of the University of Waterloo, one of the world’s leading quantum information theorists. All four courses are freely available on IBM Quantum Learning and on the Qiskit YouTube channel.

This series is genuinely university-grade material. It covers the mathematics of quantum information at the depth of a graduate quantum computing course, but is presented with exceptional clarity and is accompanied by detailed written notes for each lecture.

What you’ll learn

• Quantum information basics: state vectors, the Born rule, tensor products, and the formalism of pure quantum states reviewed with mathematical precision
• Fundamentals of quantum algorithms: the quantum circuit model, complexity classes, quantum query complexity, Deutsch-Jozsa, Simon’s algorithm, the quantum Fourier transform, phase estimation, Shor’s algorithm, and Grover’s algorithm, each developed in full mathematical detail
• General formulation of quantum information: density matrices as the correct description of mixed states and subsystems, partial trace, the Schmidt decomposition, purifications, and the operator-sum (Kraus) representation of quantum operations
• Quantum channels: completely positive trace-preserving (CPTP) maps, the Choi-Jamiolkowski isomorphism, channel representations, and the diamond norm as a measure of channel distinguishability
• Foundations of quantum error correction: the quantum error correction conditions, the stabilizer formalism, Pauli group, stabilizer codes, CSS codes, and the surface code introduced rigorously
• Quantum complexity theory: BQP, QMA, and their relationships to classical complexity classes, with an overview of problems believed to be hard for quantum computers

Course structure

The series is structured as four courses, each containing four lessons of 30-90 minute video lectures. Each lesson has an accompanying written document covering the same material in textbook format, including all equations, circuit diagrams, and worked examples.

Course 1: Basics of quantum information and computation. Course 2: Fundamentals of quantum algorithms. Course 3: General formulation of quantum information. Course 4: Foundations of quantum error correction.

The series has generated over 600,000 views and 96,000 hours of total watch time since launching in October 2022.

Who is this for?

• Advanced students who want graduate-level quantum information theory taught properly
• Anyone who has worked through an introductory course and wants to go deeper into the mathematical structure of quantum computing
• Researchers from adjacent fields (mathematics, physics, computer science) who want a rigorous foundation in quantum information
• Self-learners who find most quantum computing courses too shallow

Prerequisites

A solid foundation in linear algebra is essential: vector spaces, inner products, matrix decompositions (spectral theorem, singular value decomposition), and tensor products. Familiarity with complex analysis and basic probability is helpful. The introductory IBM Learning course “Basics of Quantum Information” is good preparation for Course 1, and each subsequent course builds on the previous.

Why take this course?

John Watrous is among the most respected researchers in quantum information theory, and his lecture style combines mathematical precision with clear intuition. The accompanying written notes make this a complete self-study resource equivalent to a university textbook.

The series covers material that most online courses either skip or treat superficially: density matrices, quantum channels, and the stabilizer formalism are essential for anyone working seriously with quantum computing, and they are developed here with the rigor they deserve. The fact that this is free and openly accessible is genuinely remarkable.