Quantum Computing

Lecturer: Dr A. Dawar and Dr B.C. Travaglione

No. of lectures: 8

Prerequisite courses: Continuous Mathematics, Computation Theory

Aims

The aims of the course are to introduce students to the basics of the quantum model of computation. The model will be used to study algorithms for searching and factorisation. Issues in the complexity of computation and in physical implementation will also be explored.

Lectures

• Bits and qubits. Introduction to quantum states with motivating examples. Comparison with classical discrete state systems.

• Linear algebra. Review of linear algebra. Vector spaces, linear operators, Dirac notation.

• Quantum mechanics. Postulates of quantum mechanics. Evolution and measurement. Entanglement.

• Computation and algorithms. Models of quantum computation. Quantum circuits, finite state systems, machines and algorithms.

• Quantum search. Grover's search algorithm. Analysis and lower bounds.

• Factorisation. Shor's algorithm for factorising numbers and analysis. Quantum Fourier transform.

• Physical implementations. Overview of experimental schemes for quantum computation.

• Quantum Complexity. Quantum complexity classes and their relationship to classical complexity. Comparison with probabilistic computation.

Objectives

At the end of the course students should

• understand the quantum model of computation and how it relates to quantum mechanics

• be familiar with some basic quantum algorithms and their analysis

• see how the quantum model relates to classical models of computation

Recommended books

Nielsen, M.A. & Chuang, I.L. (2000). Quantum computation and quantum information. Cambridge University Press.
Gruska, J. (1999). Quantum computing. McGraw Hill.
Kitaev, A.Y., Shen, A.H. & Vyalyi, M.N. (2002). Classical and quantum computation. AMS.