Computation on a noiseless quantum code and symmetrization

Let H be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra L. Suppose L admits a noiseless quantum code i.e., a subspace C ⊂ H annihilated by L. We show that a universal set of gates over C is obtained by any generic pair of L-invariant gates. Such gates - if not available from the outset - can be obtained by resorting to a symmetrization with respect to the group generated by L. Any computation can then be performed completely within the coding decoherence-free subspace

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One result added, to appear in Phys. Rev. A (RC) 4 pages LaTeX, no figures

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