Quantum Computation

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.

Unit description

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.

Relation to other units

This unit is a natural partner and successor to Quantum Information Theory. 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.

Learning objectives

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 algorithms

Transferable 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.

Syllabus

  1. The quantum circuit model
  2. Classical and quantum computational complexity
  3. 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
     4. Quantum error-correction
     5. A selection of more advanced or recent topics, as time permits. For example: quantum walks; measurement-based quantum computing; quantum communication complexity.

Reading and References

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, 2000

Other 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, 2014

Links to additional online resources will be provided during the unit.

Unit code: MATHM0023 
Level of study: M/7
Credit points: 10
Teaching block (weeks): 2 (13-18)
Lecturer: Dr Ashley Montanaro

Pre-requisites

MATHM5610 Quantum Information Theory or equivalent

Co-requisites

None

Methods of teaching

The unit will be delivered through lectures, problem sheets and problem classes.

Assessment methods

Formative assessment is through problem sheets discussed in problem classes. Summative assessment is through a 1.5-hour written exam (100%).

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