  An important step for photonic quantum technologies is the demonstration of a
quantum advantage through boson sampling. In order to prevent classical
simulability of boson sampling, the photons need to be almost perfectly
identical and almost without losses. These two requirements are connected
through spectral filtering, improving one leads to a decrease of the other. A
proven method of generating single photons is spontaneous parametric
downconversion (SPDC). We show that an optimal trade-off between
indistinguishability and losses can always be found for SPDC. We conclude that
a 50-photon scattershot boson-sampling experiment using SPDC sources is
possible from a computational complexity point of view. To this end, we
numerically optimize SPDC sources under the regime of weak pumping and with a
single spatial mode.
