A method for quantum computing uses entangled resource states which include in particular a class of highly entangled multi-particle states. These so-called cluster states can serve as a quantum computer. The resource states can be implemented with ultra-cold atoms in optical lattices or similar systems. A universal set of quantum gates, the CNOT gate and arbitrary one-system rotations, can be implemented by performing one-system measurements only. Further, a way of quantum information processing beyond the network scheme is provided.