Operator Algebras in Quantum Computation

In the following we discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science. From a computer scientist point of view, we will discuss some fundamental results of operator theory and their relevance in the context of domain theory. The theory of operator algebras originated in functional analysis in the 1930s and was extensively applied in mathematical physics, in order to understand the mathematical foundations of quantum mechanics. In the past 15 years, domain theory was successfully applied to quantum computation, for semantics and verification (see [Gay06] for an overview of the literature).