  The strong observed clustering of $z>3.5$ quasars indicates they are hosted
by massive ($M_{\rm{halo}}\gtrsim10^{12}\,h^{-1}\,\rm{M_{\odot}}$) dark matter
halos. Assuming quasars and galaxies trace the same large-scale structures,
this should also manifest as strong clustering of galaxies around quasars.
Previous work on high-redshift quasar environments, mostly focused at $z>5$,
have failed to find convincing evidence for these overdensities. Here we
conduct a survey for Lyman alpha emitters (LAEs) in the environs of 17 quasars
at $z\sim4$ probing scales of $R\lesssim7\,h^{-1}\,{\rm{Mpc}}$. We measure an
average LAE overdensity around quasars of 1.4 for our full sample, which we
quantify by fitting the quasar-LAE cross-correlation function. We find
consistency with a power-law shape with correlation length of
$r^{QG}_{0}=2.78^{+1.16}_{-1.05}\,h^{-1}\,{\rm{cMpc}}$ for a fixed slope of
$\gamma=1.8$. We also measure the LAE auto-correlation length and find
$r^{GG}_{0}=9.12^{+1.32}_{-1.31}\,h^{-1}$\,cMpc ($\gamma=1.8$), which is $3.3$
times higher than the value measured in blank fields. Taken together our
results clearly indicate that LAEs are significantly clustered around $z\sim4$
quasars. We compare the observed clustering with the expectation from a
deterministic bias model, whereby LAEs and quasars probe the same underlying
dark matter overdensities, and find that our measurements fall short of the
predicted overdensities by a factor of 2.1. We discuss possible explanations
for this discrepancy including large-scale quenching or the presence of excess
dust in galaxies near quasars. Finally, the large cosmic variance from
field-to-field observed in our sample (10/17 fields are actually underdense)
cautions one from over-interpreting studies of $z\sim6$ quasar environments
based on a single or handful of quasar fields.
