  GKP states, introduced by Gottesman, Kitaev, and Preskill, are continuous
variable logical qubits that can be corrected for errors caused by phase space
displacements. Their experimental realization is challenging, in particular
using propagating fields, where quantum information is encoded in the
quadratures of the electromagnetic field. However, travelling photons are
essential in many applications of GKP codes involving the long-distance
transmission of quantum information. We introduce a new method for encoding GKP
states in propagating fields using single photons, each occupying a distinct
auxiliary mode given by the propagation direction. The GKP states are defined
as highly correlated states described by collective continuous modes, as time
and frequency. We analyze how the error detection and correction protocol
scales with the total photon number and the spectral width. We show that the
obtained code can be corrected for displacements in time-frequency phase space
- which correspond to dephasing, or rotations, in the quadrature phase space -
and to photon losses. Most importantly, we show that generating two-photon GKP
states is relatively simple, and that such states are currently produced and
manipulated in several photonic platforms where frequency and time-bin biphoton
entangled states can be engineered.
