Scalable method for demonstrating the Deutsch-Jozsa and Bernstein-Vazirani algorithms using cluster states

We show that fundamental versions of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms can be performed using a small entangled cluster state resource of only six qubits. We then investigate the minimal resource states needed to demonstrate general n-qubit versions and a scalable method to produce them. For this purpose, we propose a versatile photonic on-chip setup.