Decoherence-free subspaces for multiple-qubit errors. II. Universal, fault-tolerant quantum computation - art. no. 022307

Decoherence-free subspaces (DFSs) shield quantum information from errors in duced by the interaction with an uncontrollable environment. Here we study a model of correlated errors forming an Abelian subgroup (stabilizer) of th e Pauli group (the group of tensor products of Pauli matrices). Unlike prev ious studies of DFSs, this type of error does not involve any spatial symme try assumptions on the system-environment interaction. We solve the problem of universal, fault-tolerant quantum computation on the associated class o f DFSs. We do so by introducing a hybrid DFS quantum error-correcting-code approach, where errors that arise due to departure of the codewords from th e DFS are corrected actively.