Photons, acting as ``flying qubits'' in propagation geometries such as waveguides, appear unavoidably in the form of wavepackets (pulses). The actual shape of the photonic wavepacket, as well as possible temporal/spectral correlations between the photons, play a critical role in successful scalable computation. Currently, unentangled indistinguishable photons are considered as a suitable resource for scalable photonic circuits. Here we show that using so called coherent photon conversion, it is possible to construct flying-qubit gates, which are not only insensitive to waveshapes of the photons and temporal/spectral correlations between them, but which also fully preserve these waveshapes and correlations upon the processing. This allows using photons with correlations and purity in a very broad range for a scalable computation. Moreover, such gates can process entangled photonic wavepackets even more effectively than unentangled ones.