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.