Quantum Computation 2019

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 at 11am Tuesday (Maths SM2), 10am Wednesday (Maths SM2) and 2pm Thursday (Maths SM1).

The drop-in session (office hour) will be 1.30pm-2.30pm Tuesday. 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 main lecture notes.
The lecture notes from the guest lecture by Dominic Verdon.
Slides about Grover's algorithm.
Exercise sheet 1 (due Tue 5th Feb); answers
Exercise sheet 2 (due Tue 12th Feb); answers
Exercise sheet 3 (due Tue 19th Feb); answers
Exercise sheet 4 (due Tue 26th Feb); answers
Exercise sheet 5 (due Tue 5th March); answers
Exercise sheet 6 (due Tue 12th March); answers
Guide to examinable material
Further practice questions; answers

Tentative schedule:

Week commencing Tuesday 11am Wednesday 10am Thursday 2pm

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

4 Feb Grover's algorithm Grover's algorithm (ctd) Discuss exercises 1
Extensions of Grover's algorithm

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

18 Feb Approximate periodicity Phase estimation Discuss exercises 3
Hamiltonian simulation

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

4 Mar Quantum error-correction
Discuss exercises 5
Quantum error-correction (ctd) Guest lecture: Fault tolerant quantum computation (Dominic Verdon)

Assessment: Exercise sheets will be provided and discussed in problems classes. Final assessment for the unit will be a 1.5-hour written exam. Past exam papers are available on the School of Mathematics student intranet.