Virtual qubits: Multilevels instead of multiparticles

The possibility of using multilevel quantum systems with a discrete nonequidistant spectrum for the physical implementation of a universal collection of quantum gates, which is required for constructing an arbitrary algorithm for a quantum computer, is studied on the basis of the proposed virtual-spin formalism. It is shown that such a set of gates, including two-qubit gates, can be constructed on a single spin-3/2 nucleus. The assertion that three-qubit gates can also be realized on a single spin-7/2 quantum particle is substantiated.