Generation of a 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 by Gottesman et al. [Phys. Rev. A 64 012310 (2001)10.1103/PhysRevA.64.012310]. 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 circuit-like and measurement-based architectures.