Constraints on primordial non-Gaussianity from 800,000 photometric
  quasars
  We derive robust constraints on primordial non-Gaussianity (PNG) using the
clustering of 800,000 photometric quasars from the Sloan Digital Sky Survey in
the redshift range $0.5<z<3.5$. These measurements rely on the novel technique
of {\it extended mode projection} to control the impact of spatially-varying
systematics in a robust fashion, making use of blind analysis techniques. This
allows the accurate measurement of quasar halo bias at the largest scales,
while discarding as little as possible of the data. The standard local-type PNG
parameters $f_\mathrm{NL}$ and $g_\mathrm{NL}$ both imprint a $k^{-2}$
scale-dependent effect in the bias. Constraining these individually, we obtain
$-49<f_\mathrm{NL}<31$ and $-2.7\times10^5<g_\mathrm{NL}<1.9\times10^5$, while
their joint constraints lead to $-105<f_\mathrm{NL}<72$ and
$-4.0\times10^5<g_\mathrm{NL}<4.9\times10^5$ (all at 95% CL) . Introducing a
running parameter $n_{f_\mathrm{NL}}$ to constrain $b(k) \propto
k^{-2+n_{f_\mathrm{NL}}}$ and a generalised PNG amplitude
$\tilde{f}_\mathrm{NL}$, we obtain $-45.5 \exp({3.7\, n_{f_\mathrm{NL}}}) <
\tilde{f}_\mathrm{NL} < 34.4 \exp({3.3\, n_{f_\mathrm{NL}}})$ at 95% CL. These
results incorporate uncertainties in the cosmological parameters, redshift
distributions, shot noise, and the bias prescription used to relate the quasar
clustering to the underlying dark matter. These are the strongest constraints
obtained to date on PNG using a single population of large-scale structure
tracers, and are already at the level of pre-{\it Planck} constraints from the
cosmic microwave background. A conservative forecast for a {\it Large Synoptic
Survey Telescope}-like survey incorporating mode projection yields
$\sigma(f_\mathrm{NL}) \sim 5$ -- competitive with the {\it Planck} result --
highlighting the power of upcoming large scale structure surveys to probe the
initial conditions of the universe.
