Decoherence-Free Subspaces for Quantum Computation

Abstract

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