Boson Sampling schemes for post-selected multi-photon gates

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.
Comment: 23 pages, 6 figures