Generation of time-frequency grid state with integrated biphoton frequency combs

Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed in [1]. We show how to experimentally implement this encoding using time-frequency continuous degrees of freedom of photon pairs produced by spontaneous parametric down conversion. We illustrate our results using an integrated AlGaAs photon-pair source. We show how single qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in a circuit-like and in a measurement-based architecture.