Exact sampling beyond Fock inputs and linear optics: photon-number superpositions, photonic matrix-product states, adaptive and non-linear circuits

arXiv:2611.11044v1 Announce Type: new Abstract: Clifford and Clifford's algorithm samples single-photon boson sampling exactly, one output mode at a time, by adding the input photons in a uniformly random order. We extend this construction to other input states and to adaptive and non-linear circuits. It applies whenever non-negative weights on output prefixes and input sets satisfy one marginal identity, a set-chain lemma: the random-order sampler is then exact at one weight evaluation per candidate mode, and it gives the posterior over the hidden input set. We build four exact samplers on it. For sources in a superposition of vacuum and one photon, the weights are rectangular permanents on an offset input set, and the cost has the exponent of single photons under loss.