All-Photonic 2xN Cluster States in Frequency, Time and Polarization

Complex and multi-dimensional cluster states of light are a critical resource for one-way quantum computers. We exploit the frequency, time and polarization domains to generate all-photonic cluster-states in a two-dimensional, 2N qubit, in a 2xN configuration. Cluster states of two dimensions or higher can serve as a resource for universal measurement-based quantum computation, and our approach allows for the realization of measurement-based two-qubit operations in an all-photonic platform. To generate the cluster states, we employ a process in which we construct dual-rail cluster states in time, frequency and polarization, as sequences of dual-color photon pairs encoded in polarization. The demonstrated discrete-variable, multi-photon, 4- and 6-qubit 2xN cluster states are shown to have high lower-bound fidelities of 0.84 and 0.57, respectively. By implementing more frequency bins the cluster state can be extended further, as well as the use of additional photonic degrees of freedom (like spatial modes) for higher dimensional cluster-states.