Photon distillation schemes with reduced resource costs based on multiphoton Fourier interference

We present a scalable scheme to achieve photon distillation, i.e. the preparation of a single photon with reduced indistinguishability error out of multiple imperfect photons, based on multiphoton interference in Fourier matrices. Our scheme achieves arbitrary error reduction in a single step, removing the need to concatenate multiple rounds of the protocol. Our scheme has resource costs linear in the error reduction, and a constant probability of success for arbitrary error reductions. We find that the scheme both raises the threshold of error correcting codes in photonic quantum computers, as well as reduces the resources required to construct a photonic quantum computer, making it highly promising for implementation in such devices.