  We show how to use Boson Sampling schemes in order to create photonic
post-selected Controlled-Z and Controlled-Controlled-Z gates, which are
equivalent, modulo single-qubit gates, to Controlled-NOT and Toffoli gates,
respectively. The new proposed method is based on the following ingredients:
identical single photons, Mach-Zehnder interferometer networks, single-photon
detectors and post-selection. In particular, by using dual-rail path encoding
together with auxiliary paths and single photons, we improve the success
probabilities of such gates. This result further proves the complexity and
richness of Reck and Clements schemes beyond the usual notions and practices of
Boson Sampling.
