Dynamical generation of noiseless quantum subsystems

We combine dynamical decoupling and universal control methods for open quan tum systems with coding procedures. By exploiting a general algebraic appro ach, we show how appropriate encodings of quantum states result in obtainin g universal control over dynamically generated noise-protected subsystems w ith limited control resources. In particular, we provide a constructive sch eme based on two-body Hamiltonians for performing universal quantum computa tion over large noiseless spaces which can be engineered in the presence of arbitrary linear quantum noise.