  The notion of symmetry is shown to be at the heart of all error
correction/avoidance strategies for preserving quantum coherence of an open
quantum system S e.g., a quantum computer. The existence of a non-trivial group
of symmetries of the dynamical algebra of S provides state-space sectors immune
to decoherence. Such noiseless sectors, that can be viewed as a noncommutative
version of the pointer basis, are shown to support universal quantum
computation and to be robust against perturbations. When the required symmetry
is not present one can generate it artificially resorting to active
symmetrization procedures.
