High-level methods for quantum computation and information

Abstract

Quantum information and computation is concerned with the use of quantum-mechanical systems to carry out computational and information-processing tasks (Nielsen and Chunag, 2000). In the few short years that this approach has been studied, a number of remarkable concepts and results have emerged, most notably:a couple of spectacular algorithms and a number of information protocols, exemplified by quantum teleportation, which exploit quantum entanglement in an essential fashion. The current tools available for developing quantum algorithms and protocols are deficient on two main levels: firstly, they are too low-level and at a more fundamental level, the standard mathematical framework for quantum mechanics (which is essentially due to von Neumann (1932)) is actually insufficiency comprehensive for informatic purposes. In joint work with Bob Coecke, we have recently made some striking progress in addressing both these points. They have recast the von Neumann formalism at a more abstract and conceptual level, using category theory.