Symmetrizing evolutions

We introduce quantum procedures for making G-invariant the dynamics of an arbitrary quantum system S, where G is a finite group acting on the space state of S. Several applications of this idea are discussed. In particular when S is a N-qubit quantum computer interacting with its environment and G the symmetric group of qubit permutations, the resulting effective dynamics admits noiseless subspaces. Moreover it is shown that the recently introduced iterated-pulses schemes for reducing decoherence in quantum computers fit in this general framework. The noise-inducing component of the Hamiltonian is filtered out by the symmetrization procedure just due to its transformation properties. (C) 1999 Published by Elsevier Science B.V. All rights reserved.