Symmetrizing evolutions

We introduce quantum procedures for making G-invariant the dynamics of an a rbitrary quantum system S, where G is a finite group acting on the space st ate of S. Several applications of this idea are discussed. In particular wh en S is a N-qubit quantum computer interacting with its environment and G t he symmetric group of qubit permutations, the resulting effective dynamics admits noiseless subspaces. Moreover it is shown that the recently introduc ed iterated-pulses schemes for reducing decoherence in quantum computers fi t in this general framework. The noise-inducing component of the Hamiltonia n is filtered out by the symmetrization procedure just due to its transform ation properties. (C) 1999 Published by Elsevier Science B.V. All rights re served.