  Using ~300,000 photometrically classified quasars, by far the largest quasar
sample ever used for such analyses, we study the redshift and luminosity
evolution of quasar clustering on scales of ~50 kpc/h to ~20 Mpc/h from
redshifts of z~0.75 to z~2.28. We parameterize our clustering amplitudes using
realistic dark matter models, and find that a LCDM power spectrum provides a
superb fit to our data with a redshift-averaged quasar bias of b_Q =
2.41+/-0.08 ($P_{<\chi^2}=0.847$) for $\sigma_8=0.9$. This represents a better
fit than the best-fit power-law model ($\omega = 0.0493\pm0.0064\theta^
{-0.928\pm0.055}$; $P_{<\chi^2}=0.482$). We find b_Q increases with redshift.
This evolution is significant at >99.6% using our data set alone, increasing to
>99.9999% if stellar contamination is not explicitly parameterized. We measure
the quasar classification efficiency across our full sample as a = 95.6 +/-
^{4.4}_{1.9}%, a star-quasar separation comparable with the star-galaxy
separation in many photometric studies of galaxy clustering. We derive the mean
mass of the dark matter halos hosting quasars as MDMH=(5.2+/-0.6)x10^{12}
M_solar/h. At z~1.9 we find a $1.5\sigma$ deviation from luminosity-independent
quasar clustering; this suggests that increasing our sample size by a factor of
1.8 could begin to constrain any luminosity dependence in quasar bias at z~2.
Our results agree with recent studies of quasar environments at z < 0.4, which
detected little luminosity dependence to quasar clustering on proper scales >50
kpc/h. At z < 1.6, our analysis suggests that b_Q is constant with luminosity
to within ~0.6, and that, for g < 21, angular quasar autocorrelation
measurements are unlikely to have sufficient statistical power at z < 1.6 to
detect any luminosity dependence in quasars' clustering.
