The quantum extension of the Geometric Machine Model ∗

extends the Geometric Machine [6] Model to ob-tain a semantic modelling of quantum algorithms related to the multi-dimensional Hilbert Space [3], involving possibly infinite synchronous and non-deterministic computations based on the spatial dis-tribution of the memory states. The QGM Model provides representation for classical and quantum superposition, including entangled pairs of quan-tum bits. We take use of the advantages of the Girard’s Coherence Space [2] to obtain the domain-theoretic ordered structure of the QGM Model as an applica-tion of the Distributed Geometric Machine [5], with a transfinite global memory shared by quantum pro-cesses distributed in a enumerable set of Geometri