| Unit name | Quantum Computation |
|---|---|
| Unit code | MATHM0023 |
| Credit points | 10 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 2C (weeks 13 - 18) |
| Unit director | Professor. Montanaro |
| Open unit status | Not open |
| Pre-requisites |
MATHM5610 Quantum Information Theory or equivalent. |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
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.
Unit aims
The unit will enable the student to understand and appreciate the concepts behind the model of quantum computation, key quantum algorithms and their applications, at a suitable level of mathematical rigour. It will also encompass theoretical subjects that are relevant to implementations of quantum computation. The unit will include topics that are currently the subject of active research and should provide suitably able and inclined students with the necessary background for postgraduate study in the field.
Relation to other units
This unit is a natural partner and successor to MATHM5610 Quantum Information Theory, which is its only prerequisite. It is likely to be of interest to students from Mathematics, Physics and Computer Science who have an interest in quantum information or the theory of computation.
Syllabus
- The quantum circuit model - Classical and quantum computational complexity - Important quantum algorithms, selected from: - Early quantum algorithms such as the Deutsch-Jozsa algorithm - Grover’s algorithm for unstructured search - Shor’s algorithm for integer factorisation - Quantum phase estimation and its applications - Simulation of quantum systems - Quantum error-correctionA selection of more advanced or recent topics, as time permits. For example: quantum walks; measurement-based quantum computing; quantum communication complexity.
At the end of the unit, a successful student will be able to:
- solve computational problems posed within the quantum computing model - apply some key quantum algorithms and prove their correctness - analyse the behaviour of previously unseen quantum circuits, algorithms and protocols - develop simple new quantum algorithmsTransferrable skills:
- Problem-solving techniques. - Rigorous mathematical thinking about computation. - The ability to assimilate and synthesize complex and novel ideas from a wide variety of areas of science.The unit will be delivered through lectures, comprising 15 hours in total, of 2-3 hours per week. There will in addition be problem sheets and 3 problem classes.
Formative assessment is through problem sheets discussed in problem classes. Summative assessment is through a 1.5-hour written exam (100%).
A good textbook that covers most of the topics in the unit is:
- M. Nielsen and I. Chuang, Quantum Computation and Quantum Information Theory, Cambridge University Press, 2000Other textbooks which may be useful or interesting include:
- A. Kitaev, A. Shen and M. Vyalyi. Classical and Quantum Computation, American Mathematical Society, 2002 - S. Aaronson, Quantum Computing Since Democritus, Cambridge University Press, 2014Links to additional online resources will be provided during the unit.
