“Hypercomputation”, that is the realization of a infinite number of calculation steps within a finite time interval, is generally assumed not feasible for it would require an exponentially increasing quantity of energy due to dissipation of the computational process. Nevertheless, we have already shown that this issue could be theoretically overcame by considering imaginary mass particles that, according to Heisenberg’s uncertainty principle, can allow the realization of “accelerated" Turing machines, i.e. computational devices capable to perform a countable infinite number of calculations in a limited time interval. On the other hand, according to quantum field theory, a system composed of many elementary atomic/molecular components, under specific density and pressure conditions, carries out a phase transition toward a coherent state in which the matter fields oscillate in tune with a self-generated electromagnetic field inside macroscopic quantum domains, called “coherent domains” (CDs), whose dimension corresponds to the wavelength of the tuning electromagnetic field. The QED coherent dynamics predicts the frequency rescaling of the coherent e.m. field inside CDs so that they behave as a self-produced cavities for the e.m. field because of the well-known Anderson – Higgs – Kibble mechanism according to which the photons belonging to the trapped e.m. field (evanescent photons) acquire an imaginary mass, becoming so unable to leave the CD. Such photons can also move without dissipation through close CDs by quantum tunneling at a very high speed and this process can be further enhanced by enclosing coherent domains inside metamaterials. Numerical calculations has been performed confirming the model predictions. In this paper we propose a novel approach based on the QED coherent dynamics, for developing a hyper-computing system, able to overcome the “Turing barrier” and then suitable to open very interesting prospects for the realization of several technological applications as, for example, the achievement of the so-called “strong” or general artificial intelligence.