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We represent the realization of Grover search algorithm on the states of atoms in optical cavities. We improved the scheme of H.Azuma for the CNOT gate and realized it by only one cavity instead of two. We also estimated the effect of the main source of decoherence - the broadening of spectral line from the photon exchange between cavities, which issues from the uncertainty relation "time-energy" and established the maximal number of qubits for which it is possible to make GSA on this technology.