We propose an effective set of elementary quantum gates which provide an encoded universality and demonstrate the physical feasibility of these gates for the solid-state quantum computer based on the multi-atomic systems in the QED cavity. We use the two-qubit encoding and swapping-based operations to simplify a physical realization of universal quantum computing and add the immunity to a number of errors. This approach allows to implement any encoded single-qubit operation by three elementary gates and the encoded controlled- NOT operation can be performed in a single step. The considerable advantages are also shown for implementing some commonly used controlled gates.
@article{arxiv.1109.0291,
title = {Encoded Universality of Quantum Computations on the Multi-Atomic Ensembles in the QED Cavity},
author = {Farid Ablayev and Sergey Andrianov and Sergey Moiseev and Alexander Vasiliev},
journal= {arXiv preprint arXiv:1109.0291},
year = {2011}
}