The light’s image is the primary source of information carrier in nature. Indeed, a single photon’s image possesses a vast information capacity that can be harnessed for quantum information processing. Our scheme for implementing quantum information processing on a discretized photon wavefront via universal multiport processors employs a class of quantum Fourier optical systems composed of spatial phase modulators and 4f-processors with phase-only pupils having a characteristic periodicity that reduces the number of optical resources quadratically as compared to other conventional path-encoding techniques. In particular, this article employs quantum Fourier optics to implement some key quantum logical gates that can be instrumental in optical quantum computations. For instance, we demonstrate the principle by implementing the single-qubit Hadamard and the two-qubit controlled- not gates via simulation and optimization techniques. Due to various advantages of the proposed scheme, including the large information capacity of the photon wavefront, a quadratically reduced number of optical resources compared with other conventional path-encoding techniques, and dynamic programmability, the proposed scheme has the potential to be an essential contribution to linear optical quantum computing and optical quantum signal processing.