  The Sloan Digital Sky Survey has surveyed 14,555 square degrees of the sky,
and delivered over a trillion pixels of imaging data. We present the
large-scale clustering of 1.6 million quasars between z = 0.5 and z = 2.5 that
have been classified from this imaging, representing the highest density of
quasars ever studied for clustering measurements. This data set spans ~11,000
square degrees and probes a volume of 80(Gpc/h)^3. In principle, such a large
volume and medium density of tracers should facilitate high-precision
cosmological constraints. We measure the angular clustering of photometrically
classified quasars using an optimal quadratic estimator in four redshift slices
with an accuracy of ~25% over a bin width of l ~10 - 15 on scales corresponding
to matter-radiation equality and larger (l ~ 2 - 30). Observational systematics
can strongly bias clustering measurements on large scales, which can mimic
cosmologically relevant signals such as deviations from Gaussianity in the
spectrum of primordial perturbations. We account for systematics by employing a
new method recently proposed by Agarwal et al. (2014) to the clustering of
photometrically classified quasars. We carefully apply our methodology to
mitigate known observational systematics and further remove angular bins that
are contaminated by unknown systematics. Combining quasar data with the
photometric luminous red galaxy (LRG) sample of Ross et al. (2011) and Ho et
al. (2012), and marginalizing over all bias and shot noise-like parameters, we
obtain a constraint on local primordial non-Gaussianity of fNL = -113+/-154
(1\sigma error). [Abridged]
