Books and courses
Understanding Quantum Information and Computation
This is a course on the theory of quantum computing, consisting of 16 lessons divided into four units, with each lesson including a video and a written component. The course covers subject matter roughly corresponding to a one-semester university course at the advanced undergraduate or introductory graduate level.
Written material
- Download all 16 lessons as a single file [pdf]
- Find four courses named for the four units from Quantum learning on the IBM Quantum Platform:
Videos and slides
Videos are available on the Qiskit YouTube channel as a playlist or individually by lesson. Slides used to create the videos, in pdf format, are also available for each lesson.
- Single Systems [YouTube, pdf]
- Multiple Systems [YouTube, pdf]
- Quantum Circuits [YouTube, pdf]
- Entanglement in Action [YouTube, pdf]
- Quantum Query Algorithms [YouTube, pdf]
- Quantum Algorithmic Foundations [YouTube, pdf]
- Phase Estimation and Factoring [YouTube, pdf]
- Grover’s Algorithm [YouTube, pdf]
- Density Matrices [YouTube, pdf]
- Quantum Channels [YouTube, pdf]
- General Measurements [YouTube, pdf]
- Purifications and Fidelity [YouTube, pdf]
- Correcting Quantum Errors [YouTube, pdf]
- The Stabilizer Formalism [YouTube, pdf]
- Quantum Code Constructions [YouTube, pdf]
- Fault-Tolerant Quantum Computation [YouTube, pdf]
Archival material
This course is partially based on a course I taught at the University of Calgary many years ago. I strongly recommend the written material linked above over the notes for this course, but if you’re looking for these course notes specifically they are available here as a single document (139 pages). [pdf]
The Theory of Quantum Information
This book was published by Cambridge University Press in April 2018, and is available for purchase through the publisher and other standard distribution channels. A manuscript version of the book can be found below — it has been made available for personal use only and must not be sold or redistributed.
Errata [pdf]
Complete book
Individual chapters (standard layout)
- Mathematical preliminaries [pdf]
- Basic notions of quantum information [pdf]
- Similarity and distance among states and channels [pdf]
- Unital channels and majorization [pdf]
- Quantum entropy and source coding [pdf]
- Bipartite entanglement [pdf]
- Permutation invariance and unitarily invariant measures [pdf]
- Quantum channel capacities [pdf]
Individual chapters (compact layout)
- Mathematical preliminaries [pdf]
- Basic notions of quantum information [pdf]
- Similarity and distance among states and channels [pdf]
- Unital channels and majorization [pdf]
- Quantum entropy and source coding [pdf]
- Bipartite entanglement [pdf]
- Permutation invariance and unitarily invariant measures [pdf]
- Quantum channel capacities [pdf]
Archival material
This book grew out of lecture notes for a course having a similar name that I taught many times at the University of Waterloo. I strongly recommend the book over the course notes, but if you’re looking for the lecture notes specifically they are available here as a single document (197 pages). [pdf]
Introduction to the Theory of Computing
These are lecture notes for a traditional undergraduate course on the theory of computing covering finite automata, context-free grammars, and Turing machines that I taught at the University of Waterloo many times, most recently in Spring 2019.
Lecture notes
All 20 lectures in one file (227 pages) [pdf]
- Course overview and mathematical foundations [pdf]
- Countability for languages; deterministic finite automata [pdf]
- Nondeterministic finite automata [pdf]
- Regular operations and regular expressions [pdf]
- Proving languages to be nonregular [pdf]
- Further discussion of regular languages [pdf]
- Context-free grammars and languages [pdf]
- Parse trees, ambiguity, and Chomsky normal form [pdf]
- Properties of context-free languages [pdf]
- Proving languages to be non-context free [pdf]
- Pushdown automata [pdf]
- Turing machines [pdf]
- Variants of Turing machines [pdf]
- Stack machines [pdf]
- Encodings; examples of decidable languages [pdf]
- Universal Turing machines and undecidable languages [pdf]
- More undecidable languages; reductions [pdf]
- Further discussion of computability [pdf]
- Time-bounded computations [pdf]
- NP, polynomial-time mapping reductions, and NP-completeness [pdf]
Latest update: October 19, 2020
Advanced Topics in Quantum Information Theory
This was an advanced graduate course on quantum information theory, including video lectures and notes, taught online (unexpectedly and by necessity) in Spring 2020. The videos took a long time to create and I only managed to cover about half of the material I had intended for the course.
Lecture notes
All 8 lectures in one file (106 pages) [pdf]
- Conic programming [pdf]
- Max-relative entropy and conditional min-entropy [pdf]
- Smoothing and optimizing max-relative entropy [pdf]
- Regularization of the smoothed max-relative entropy [pdf]
- Min-relative entropy, conditional max-entropy, and hypothesis-testing relative entropy [pdf]
- Nonlocal games and Tsirelson’s theorem [pdf]
- A semidefinite program for the entangled bias of XOR games [pdf]
- The hierarchy of Navascues, Pironio, and Acin [pdf]
Latest update: March 14, 2021
Videos
- Conic programming [YouTube]
- Max-relative entropy and conditional min-entropy [YouTube]
- Smoothing and optimizing max-relative entropy [YouTube]
- Regularization of the smoothed max-relative entropy [YouTube]
- Min-relative entropy, conditional max-entropy, and hypothesis-testing relative entropy [YouTube]
- Nonlocal games and Tsirelson’s theorem [YouTube]
- A semidefinite program for the entangled bias of XOR games [YouTube]
- The hierarchy of Navascues, Pironio, and Acin [YouTube]