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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.
Next: Topics in Concurrency
Up: Lent Term 2004: Part
Previous: Optimising Compilers
  Contents
Christine Northeast
Thu Sep 4 15:29:01 BST 2003