**Strategies for measurement-based quantum computation with SLOCC-transformed cluster states**

Universal quantum computation can be accomplished via projective single-qubit measurements on a highly entangled resource state, together with classical feedforward of the measurement results. The best-known example of such a resource state is the cluster state, on which judiciously chosen single-qubit measurements can be used to simulate an arbitrary quantum circuit with a number of measurements that is linear in the number of gates. We examine the power of the orbit of cluster states under GL(2,C), also known as the SLOCC-equivalence class, as a resource for universal computation driven strictly by projective measurements. We identify circumstances under which such states constitute resources for random-length computation, in one case quasi-deterministically and in another probabilistically.