  We propose an effective realization of a complete set of elementary quantum
gates in the solid-state quantum computer based on the multi-atomic coherent
(MAC-) ensembles in the QED cavity. Here, we use the two-ensemble qubit
encoding and swapping-based operations that together provide implementation of
any encoded single-qubit operation by three elementary gates and the encoded
controlled-NOT operation is performed in a single step. This approach
simplifies a physical realization of universal quantum computing and adds the
immunity to a number of errors. We also demonstrate that the proposed
architecture of quantum computer satisfies DiVincenzo criteria.

Quantum Physics