  The boson sampler proposed by Aaronson and Arkhipov is a non-universal
quantum computer, which can serve as evidence against the extended
Church-Turing thesis. It samples the probability distribution at the output of
linear unitary optical network, with indistinguishable single photons at the
input. Four experimental groups have already tested their small-scale
prototypes with up to four photons. The boson sampler with few dozens of single
photons is believed to be hard to simulate on a classical computer. For
scalability of a realistic boson sampler with current technology it is
necessary to know the effect of the photon mode mismatch on its operation. Here
a nondeterministic model of the boson sampler is analyzed, which employs
partially indistinguishable single photons emitted by identical sources. A
sufficient condition on the average mutual fidelity $ \langle
\mathcal{F}\rangle$ of the single photons is found, which guarantees that the
realistic boson sampler outperforms the classical computer. Moreover, the boson
sampler computer with partially indistinguishable single photons is scalable
while being beyond the power of classical computers when the single photon mode
mismatch $1-\langle \mathcal{F}\rangle$ scales as $ \mathcal{O}(N^{-3/2})$ with
the total number of photons $N$.
