  A quantum computing system is typically represented by a set of
non-interacting (local) two-state systems - qubits. Many physical systems can
naturally have more accessible states, both local and non-local. We show that
the resulting non-local network of states connecting qubits can be efficiently
addressed via continuous time quantum random walks, leading to substantial
speed-up of multiqubit entanglement manipulations. We discuss a three-qubit
Toffoli gate and a system of superconducting qubits as an illustration.
