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Boson sampling is one of the leading protocols for demonstrating a quantum advantage, but the theory of how this protocol responds to noise is still incomplete. We extend the theory of classical simulation of boson sampling with partial distinguishability to the case where the degree of indistinguishability between photon pairs is different between different pairs.

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., Comment: 13 pages, 11 figures. Related work in arXiv:2404.14217