Physical computation and compositionality

Developments in quantum computing and, more in general, non-standard computing systems, represent a clear indication that the very notion of what a physical computing device is and does should be recast in a rigorous and sound framework. Physical computing has opened a whole stream of new research aimed to understand and control how information is processed by several types of physical devices. Therefore, classical definitions and entire frameworks need to be adapted in order to fit a broader notion of what physical computing systems really are. Recent studies have proposed a formalism that can be used to carve out a more proper notion of physical computing. In this paper we present a framework which capture such results in a very natural way via some basic constructions in Category Theory. Furthermore, we show that, within our framework, the compositional nature of physical computing systems is naturally formalized, and that it can be organized in coherent structures by the means of their relational nature.