Description of state and quantum nature of hydrogen subsystem, represented by supramolecular polycondensate on nanotubular surface, is the problem of particular interest. One has to consider that theoretical approaches based on both physical sorption due to Van der Waals interaction and chemisorption with covalent bonding seem to be unsatisfactory when dealing with high-performance reversible hydrogen polycondensation. The main consequence obtained under such circumstances is inapplicability of molecular orbital approach to description of interaction between hydrogen and adsorbing surface. Our consideration of the state and of the nature of bonding of subsurface molecules H2 proceeds from the results of non-empirical calculations via approximating quasiparticle density functional method. The state of hydrogen is described by active bi-radical state of dimer H-H. There are quasielectron density has a localized one-centered distribution in hydrogen molecule. Evidently, this fact is determined for hydrogen intermolecular interaction the examination of two cases of spin multiplicity: singlet and triplet. The selection of an optimal spin configuration for the hydrogen layer is carried out by iteration procedure of the total binding energy minimization within the framework of spin-flip dynamics. The nature of contact exchange interaction, typical for the systems with finite density distribution, is revealed within the framework of quantum-field concepts of matter structure. We model a relaxation phase being comprised in evolution of hydrogen polycondensate from the position of the approach to stochastic dissipative dynamics. It is taking into account, that decoherence frequency depends on parameters of polycondensate quantum plasma and on temperature. Several cases of adsorption contact of hydrogen with both external and internal nanotubular surfaces are presented. On the basis of received we forecast the possibility of using carbon nanotubes as hydrogen medium storage.