Quantum Computation

Ashley Montanaro

Quantum computers are machines that are designed to use the principles of quantum mechanics to do things that cannot be done by any standard computer based only on classical physics. This unit will introduce the emerging theory of quantum computation, which has many remarkable features compared with classical computation. The unit will cover some of the most important quantum algorithms currently known, which outperform classical algorithms for tasks ranging from factorising large integers to simulating large quantum-mechanical systems.

Lectures and problem classes will be held in Physics 3.21 at 11am Monday, 9am Tuesday and 11am Friday.

The drop-in session (office hour) will be Mondays, 9.30-10.30am. Ashley's office is room 3.8 in the main Maths building.

Materials

The materials from Quantum Information Theory will be useful and this unit will generally follow the same notation. You may also find some excellent revision notes by Richard Jozsa useful.
The lecture notes.
Slides about Grover's algorithm.
Exercise sheet 1 (due Wed 31st Jan); answers
Exercise sheet 2 (due Wed 7th Feb); answers
Exercise sheet 3 (due Wed 14th Feb); answers
Exercise sheet 4 (due Wed 21st Feb); answers
Exercise sheet 5 (due Wed 28th Feb); answers
Exercise sheet 6 (due Wed 7th March); answers
Guide to examinable material
Further practice questions; answers

Tentative schedule:

Week commencing Monday 11am Tuesday 9am Friday 11am

22 Jan Introduction
Computational complexity The quantum circuit model Oracles and the Deutsch-Jozsa algorithm in the quantum circuit picture

29 Jan Grover's algorithm Grover's algorithm (ctd) Discuss exercises 1
Extensions of Grover's algorithm

5 Feb The QFT and periodicity Shor's algorithm Discuss exercises 2
Shor's algorithm (ctd)

12 Feb Approximate periodicity Phase estimation Discuss exercises 3
Hamiltonian simulation

19 Feb Hamiltonian simulation (ctd) Decoherence Discuss exercises 4
Examples of quantum channels

26 Feb Quantum error-correction
Guest lecture: Experimental quantum computing (Dr Raffaele Santagati) Discuss exercises 5
Quantum error-correction (ctd)

Assessment: Exercise sheets will be provided and discussed in problems classes. Final assessment for the unit will be a 1.5-hour written exam. An example exam question will be provided.