The works devoted to an issue of quantum computer design have been analyzed. The main problems related to creation of the quantum computer are discussed. A fundamentally new approach to solving the problem of creating a truly quantum computer based on the “up to bottom” strategy has been proposed and justified. The strategy can be implemented by preliminary visualization of the quantum states of qubits using nanotriggers formed from two-dimensional material, in particular, graphene. This refers to the visualization (materialization) of all, including entangled, states, which mainly determine the theoretically possible large mathematical resource of a quantum computer. A block-diagram of the electronic device based on “a priory” quantum states of q-bits is proposed. It is shown that for implementation of quantum computation procedure, each materialized (visualized) Shor's cell should correspond to an element of the electronic scheme. The device includes a block containing at least 1010 nanotriggers that perform a role of q-bits of quantum computation, which are created using graphene nanoribbons and controlled by a special element. The latter represents a self-organizing quantum dot having two essentially different states in terms of magnetic properties. This quantum dot is prepared on the basis of a compound, the molecules of which are characterized by the intramolular rearrangement. The nanotriggers are employed to form reversible logic blocks or gates. Each gate contains three triggers to perform logical operations. The offered device is an additional electronic unit that is embedded in a digital computer, which makes it possible to implement the computational process in accordance with the requirements of the provisions of quantum physics.