Decoherence in quantum computers is formulated within the Semigroup approach.
The error generators are identified with the generators of a Lie algebra. This
allows for a comprehensive description which includes as a special case the
frequently assumed spin-boson model. A generic condition is presented for
error-less quantum computation: decoherence-free subspaces are spanned by those
states which are annihilated by all the generators. It is shown that these
subspaces are stable to perturbations and moreover, that universal quantum
computation is possible within them.