  We investigate a scenario where primordial black holes (PBHs) can be the
progenitors of supermassive black holes (SMBHs) observed at $z\sim6$. To this
end, we carried out clustering analysis using a sample of 81 quasars at $5.88
<z<6.49$, which is constructed in Subaru High-$z$ Exploration of Low-Luminosity
Quasars (SHELLQs) project, and 11 quasars in the same redshift range selected
from the literature. The resulting angular auto-correlation function (ACF) can
be fitted to a power-law form of $\omega_\theta =
0.045^{+0.114}_{-0.106}~\theta^{-0.8}$ over a scale of $0.2\!-\!10$ degrees. We
compare the ACF of the quasars to that predicted for the PBH model at $z\sim 6$
and found that such a scenario is excluded for a broad range of parameter
space, from which we can conclude that a scenario with PBHs as SMBHs is not
viable. We also discuss a model in which SMBHs at $z \sim 6$ originate from the
direct collapse of PBH clumps and argue that the observed ACF excludes such a
scenario in the context of our PBH model.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology