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

Quantum Computing on Multi-atomic Ensembles in Quantum Electrodynamics Cavity