  The most frequently proposed model for the origin of quasars holds that the
high accretion rates seen in luminous active galactic nuclei are primarily
triggered during major mergers between gas-rich galaxies. While plausible for
decades, this model has only begun to be tested with statistical rigor in the
past few years. Here we report on a Hubble Space Telescope study to test this
hypothesis for $z=2$ quasars with high super-massive black hole masses
($M_\mathrm{BH}=10^9-10^{10}~M_\odot{}$), which dominate cosmic black hole
growth at this redshift. We compare Wide Field Camera 3 $F160W$ (rest-frame
$V$-band) imaging of 19 point source-subtracted quasar hosts to a matched
sample of 84 inactive galaxies, testing whether the quasar hosts have greater
evidence for strong gravitational interactions. Using an expert ranking
procedure, we find that the quasar hosts are uniformly distributed within the
merger sequence of inactive galaxies, with no preference for quasars in
high-distortion hosts. Using a merger/non-merger cutoff approach, we recover
distortion fractions of $f_\mathrm{m,qso}=0.39\pm{}0.11$ for quasar hosts and
$f_\mathrm{m,gal}=0.30\pm{}0.05$ for inactive galaxies (distribution modes, 68%
confidence intervals), with both measurements subjected to the same
observational conditions and limitations. The slight enhancement in distorted
fraction for quasar hosts over inactive galaxies is not significant, with a
probability that the quasar fraction is higher of
$P(f_\mathrm{m,qso}>f_\mathrm{m,gal}) = 0.78$ ($0.78\,\sigma{}$), in line with
results for lower mass and lower $z$ AGN. We find no evidence that major
mergers are the primary triggering mechanism for the massive quasars that
dominate accretion at the peak of cosmic quasar activity.
