• Notation and terminology (incomplete)
• Lecture 1: Computation and Complexity
• Lecture 2: First Algorithms
• Lecture 3: QFT and Phase Estimation
• Lecture 4: Shor's algorithm
• Lecture 5: Grover's algorithm and Amplitude Amplification
• Lecture 6: Hamiltonian Simulation
• Lecture 7: Heuristic Algorithms

• Problem sheet

The lecture notes and problem sheets are copyright ©Toby Cubitt, and are licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Quantum computing is the flagship quantum technology. Peter Shor's 1994 quantum factoring algorithm kicked off a wave of interest and excitment about quantum computing, and is in large part responsible for the field of quantum information going mainstream. A second wave of even more excitment has been kicked off recently by the near-term prospect of NISQ hardware (noisy, intermediate-scale quantum computers) – i.e. quantum computing hardware that is not obviously useful for anything… but no longer obviously useless either!

However, there is also currently a lot of hype and many unrealistic expectations. The aim of this course is to show you where all the excitment derives from, rigorously and in detail; and to innoculate you against the over-hype.

Understanding of basic quantum information theory at the level of the first term CDT quantum information course is assumed. (Qubits, density matrices, measurement, entanglement, etc.)

The appropriate sections of the following text books cover much of the course material, though not necessarily in the same way:

• Nielsen, M. and Chuang, I., "Quantum Computation and Quantum Information", Cambridge University Press
• Kitaev, A., Shen, A., and Vyalyi M. "Classical and Quantum Computation", American Mathematical Society

There are also many excellent sets of lecture notes freely available online covering this material. Some cover it in a very similar way, some take a different approach; both make for valuable additional reading!

Here's an incomplete list:

• John Watrous, Introduction to Quantum Computating
• Richard Jozsa, Quantum Information and Computation (basic material) and Quantum Computation (further material)
• Dave Bacon, Quantum Computing
• Andrew Childs, Quantum Algorithms (more advanced material than this course)
• Ashley Montanaro, Quantum Computation
• Ronald de Wolf, Quantum Computing (good if you're coming from a computer science background)