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 Wednesday 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.
  • Exercise sheet 1 (due Tue 30th Jan)

Tentative schedule:

Week commencingMonday 11amTuesday 9amFriday 11am
22 JanIntroduction
Computational complexity
The quantum circuit modelOracles and the Deutsch-Jozsa algorithm in the quantum circuit picture
29 JanGrover's algorithmGrover's algorithm (ctd)Discuss exercises 1
Extensions of Grover's algorithm
5 FebThe QFT and periodicityShor's algorithmDiscuss exercises 2
Shor's algorithm (ctd)
12 FebApproximate periodicityPhase estimationDiscuss exercises 3
Hamiltonian simulation
19 FebHamiltonian simulation (ctd)DecoherenceDiscuss exercises 4
Quantum error-correction
26 FebQuantum error-correction (ctd)

Discuss exercises 5
Experimental quantum computing


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.