  Boson sampling is a well-defined task that is strongly believed to be
intractable for classical computers, but can be efficiently solved by a
specific quantum simulator. However, an outstanding problem for large-scale
experimental boson sampling is the scalability. Here we report an experiment on
boson sampling with photon loss, and demonstrate that boson sampling with a few
photons lost can increase the sampling rate. Our experiment uses a
quantum-dot-micropillar single-photon source demultiplexed into up to seven
input ports of a 16*16 mode ultra-low-loss photonic circuit, and we detect
three-, four- and five-fold coincidence counts. We implement and validate lossy
boson sampling with one and two photons lost, and obtain sampling rates of 187
kHz, 13.6 kHz, and 0.78 kHz for five-, six- and seven-photon boson sampling
with two photons lost, which is 9.4, 13.9, and 18.0 times faster than the
standard boson sampling, respectively. Our experiment shows an approach to
significantly enhance the sampling rate of multiphoton boson sampling.
