The Semantics of Quantum Computation

Herbert Wiklicky

Imperial College

Quantum computation, i.e. the idea of performing ``computations''

using a quantum device instead of the standard classical computers,

is one of the new computational paradigms which have been emerging

over the last few years. Though it is still a highly speculative

subject - real quantum computers are still science fiction - its

conceptual and theoretical implications are quite challenging: for

cryptography, information and complexity theory, but also for

semantics.

The aim of this talk is to give an introduction and overview of the

underlying concepts and structures behind quantum computation from

a semantical point of view. To this effect we will first, and mainly,

discuss the mathematics of quantum physics, i.e. the mathematical

structures needed to formulate the laws of quantum mechanics and to

model quantum computation. This will concern in particular ``infinite

dimensional linear algebra'', i.e. functional analysis. We then will

introduce the standard model of quantum mechanics and discuss some

of its important ``non-classical'' features. Finally, we will look
at

a theoretical model for quantum computation and discuss some of its

characteristics and constraints.