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Quantum information processing requires a high degree of isolation from thedetrimental effects of the environment as well as an extremely precise level ofcontrol on the way quantum dynamics unfolds in the information-processingsystem. In this paper, we show how these two goals can be ideally achieved byhybridizing the concepts of noiseless subsystems and of holonomic quantumcomputation. An all-geometric universal computation scheme based onnon-adiabatic and non-Abelian quantum holonomies embedded in a four-qubitnoiseless subsystem for general collective decoherence is proposed. Theimplementation details of this synergistic scheme along with the analysis ofits stability against symmetry-breaking imperfections are presented.

Quantum Computation in Noiseless Subsystems with Fast Non-Abelian Holonomies