  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 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 paper 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.
