Classical Internet evolved exceptionally during the last five decades, from a
network comprising a few static nodes in the early days to a leviathan
interconnecting billions of devices. This has been possible by the separation
of concern principle, for which the network functionalities are organized as a
stack of layers, each providing some communication functionalities through
specific network protocols. In this survey, we aim at highlighting the
impossibility of adapting the classical Internet protocol stack to the Quantum
Internet, due to the marvels of quantum mechanics. Indeed, the design of the
Quantum Internet requires a major paradigm shift of the whole protocol stack
for harnessing the peculiarities of quantum entanglement and quantum
information. In this context, we first overview the relevant literature about
Quantum Internet protocol stack. Then, stemming from this, we sheds the light
on the open problems and required efforts toward the design of an effective and
complete Quantum Internet protocol stack. To the best of authors' knowledge, a
survey of this type is the first of its own. What emerges from this analysis is
that the Quantum Internet, though still in its infancy, is a disruptive
technology whose design requires an inter-disciplinary effort at the border
between quantum physics, computer and telecommunications engineering