Lecture courses

Lecture notes (mostly hand-written) for various courses I've taught (or, sometimes, attended).

Note that though I have checked the notes for typos and mistakes, this by no means guarantees there are none! If you think you've spotted one, let me know.


Creative Commons License Unless otherwise stated, all lecture notes linked from this web site are copyright ©Toby Cubitt, and are licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Quantum Computation and Complexity course

15 July 2016 Lectured at the 2016 Autrans summer school on Stochastic Methods in Quantum Mechanics. The notes are adapted from the first half my Advanced Quantum Information Theory course, with additional material on the basics of computation and complexity theory.

Lecture notes

  • Lectures 1-2: Computation and Complexity
  • Lecture 3: Local Hamiltonians
  • Lectures 3-4: Kitaev's Theorem
  • Lecture 4: Local clock construction

Recommended reading

The Arora-Barak book gives an excellent, modern treatment o

Matrix Product States and PEPS

14 July 2016 Notes from David Perez-Garcia's lecture course on Matrix Product States and PEPS at the 2016 Autrans summer school on Stochastic Methods in Quantum Mechanics.

The slides are courtesy of David. The lecture notes are my handwritten notes from the whiteboard section of David's lectures. All content by David; all mistakes by me!

Lecture notes

  • MPS motivation (slides)
  • MPS lecture notes (handwritten)
  • PEPS and topological order (slides)


(The slides are copyright © 2016 David Perez-Garcia, with all rights reserved. The handwritten notes are copyright ©{

Decoupling Method in Quantum Shannon Theory

19 October 2015 Originally lectured in 2015 as part of the quantum information theory masters course for the UCL quantum CDT.

Lecture Notes

  • Decoupling Method

Recommended reading

Much of the material covered here (and more!) was originally proven in the Mother of All Protocols paper by Abeyesinghe, Devetak, Hayden and Winter.

These notes largely follow Section 10.9 of Preskill's wonderful lecture notes, with a (very) few modifications and additions.

Advanced Quantum Information Theory course

13 March 2015 Lectured from 2013 to 2015 as a Part III Mathematics course at the University of Cambridge.

Lecture notes

  • Notation and terminology
  • Bibliography

Section 1: Hamiltonian Complexity

  • Lecture 1-2: Whistle-stop introduction to complexity theory
  • Lectures 3-4: Local Hamiltonians
  • Lectures 5-7: Kitaev's Theorem
  • Lecture 8: Local clock construction

Section 2: Lieb-Robinson techniques

  • Lecture 9: Many-body quantum physics introduction
  • Lecture 10-12: Lieb-Robinson bounds
  • Lectures 13-15: Exponential decay of correlations

Problem sheets

  • Examples sheet 1: Complexity theory; Hamiltonian complexity
  • Examples sheet 2: Kitaev's theorem; Many-body physics; Lieb-Robinson bounds

Quantum Mechanics for Mathematicians course

4 November 2011 Lectured in 2011 as the first section of a "Mathematics for Quantum Information" masters course given in the mathematics faculty of the Universidad Complutense de Madrid.

Lecture Notes

  • Section 0: Dirac notation;
    Section 1: The postulates of quantum mechanics
    (lecture 1)
  • Section 2: Combining quantum systems: tensor products
    (lecture 2)
  • Section 3: Non-locality and Bell inequalities
    (lecture 3)
  • Section 4: Ensembles and density operators;
    Section 5: Taking quantum systems apart: reduced states and the partial trace;
    Section 6: A brief introduction to entropy
    (lecture 4)

Quantum Mechanics course

11 May 2010 Lectured from 2007 to 2010 as the second part of the 3rd year mathematics undergraduate "Quantum Mechanics" course at the University of Bristol.

Lecture Notes

  • Section 1: Angular Momentum and Spin
    (lectures 1 and 2)
  • Section 2: Representations of Angular Momentum
    (lectures 3 to 5)
  • Section 3: Orbital Anglular Momentum
    (bonus lecture)
  • Section 4: Measurement
    (lecture 6)
  • Section 5: Multiple Particles and Tensor Products
    (lectures 7 and 8)
  • Section 6: Non-Locality and Bell Inequalities
    (lectures 9 and 1

Classical mechanics and electrodynamics

I have left up some of the material I prepared for classical mechanics and electrodynamics courses taught by Prof. Weise at the TUM (many, many years ago!) in case it's of use to someone.

Question Sheet Solutions

Given that the question sheets are substantially re-used in subsequent semesters, I've removed the worked solutions that were available here, to help you avoid the temptation to…ahem…short-cut the valuable learning process that struggling to solve the questions provides. (Believe it or not, the question sheets are not some obscure form of torture dreamed up by bitter and twist