  Multiphoton interference is at the very heart of quantum foundations and
applications in quantum sensing and information processing. In particular,
boson sampling experiments have the potential to demonstrate quantum
computational supremacy while only relying on multiphoton interference in
linear optical interferometers. However, even when photonic losses are
negligible, scalable experiments are challenged by the rapid decrease of the
probability of success of current schemes with probabilistic sources for a
large number of single photons in each experimental sample. Remarkably, we show
a novel boson sampling scheme where the probability of success increases
instead of decreasing with the number of input photons eventually approaching a
unit value even with non deterministic sources. This is achieved by sampling at
the same time in the number of occupied input ports and the number of input
photons per port, differently form previous schemes where the number of
occupied ports is fixed at each experimental run. Therefore, these results
provide a new exciting route toward future demonstrations of quantum
computational supremacy with scalable experimental resources.
