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We propose an effective realization of the universal set of elementaryquantum gates in solid state quantum computer based on macroscopic (ormesoscopic) resonance systems - multi-atomic coherent ensembles, squids orquantum dots in quantum electrodynamic cavity. We exploit an encoding oflogical qubits by the pairs of the macroscopic two- or three-level atoms thatis working in a Hilbert subspace of all states inherent to these atomicsystems. In this subspace, logical single qubit gates are realized by thecontrolled reversible transfer of single atomic excitation in the pair via theexchange of virtual photons and by the frequency shift of one of the atomicensembles in a pair. In the case of two-level systems, the logical two - qubitgates are performed by the controlling of Lamb shift magnitude in one atomicensemble, allowing/blocking the excitation transfer in a pair, respectively,that is controlled by the third atomic system of another pair. When usingthree-level systems, we describe the NOT-gate in the atomic pair controlled bythe transfer of working atomic excitation to the additional third level causedby direct impact of the control pair excitation. Finally, we discuss advantagesof the proposed physical system for accelerated computation of some usefulquantum gates.

Quantum computer with atomic logical qubits encoded on macroscopic three-level systems in common quantum electrodynamic cavity