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 Maths SM2 at 9am on Tuesdays, Wednesdays and Thursdays.

The drop-in session (office hour) will be Thursdays, 1.30-2.30pm. 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 Tue 31st Jan); answers
Exercise sheet 2 (due Tue 7th Feb); answers
Exercise sheet 3 (due Tue 14th Feb); answers
Exercise sheet 4 (due Tue 21st Feb); answers
Exercise sheet 5 (due Tue 28th Feb); answers
Exercise sheet 6 (due Tue 7th March); answers
Guide to examinable material
Further practice questions

Tentative schedule:

Week commencing Tuesday 9am Wednesday 9am Thursday 9am

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

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

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

13 Feb Approximate periodicity Phase estimation Discuss exercises 3
Hamiltonian simulation

20 Feb Hamiltonian simulation (ctd) Decoherence Discuss exercises 4
Quantum error-correction

27 Feb Quantum error-correction (ctd)
The stabilizer formalism The stabilizer formalism (ctd)
Discuss exercises 5 Experimental quantum computing (Dr Dylan Mahler)

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.