This article deals with nonequilibrium self-assembling and self-organizing processes of multilevel synthesis of hydrogen anode that are considered employing the methods computational nanotechnology. These processes include femtosecond quantum entanglement processing of carbon nanogel electrodes and fractal nanoparticle catalysts. This article also analyzes the results of the computer imitation of algorithmic nanoengineering of multilevel designing inside anode's nanopore of carbon nanogel nanocomposite with Ni nanoparticle catalysts. There are three levels of multilevel synthesis processing: quantum dynamics of atoms, quantum entanglement dynamics of nanosystems and classical dynamics of micropour systems. They obey the principals of self-assembling and self-organization on the level of nanosystems, that is the most basic one for self-managing operations. It demands the application of the most difficult quantum computer processing because of the corporative effects of quantum entanglement, which comply with specific quantum information processing. (C) 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.