Evidence for Low Radiative Efficiency or Highly Obscured Growth of $z>7$
  Quasars
  The supermassive black holes (SMBHs) observed at the centers of all massive
galaxies are believed to have grown via luminous accretion during quasar phases
in the distant past. The fraction of inflowing rest mass energy emitted as
light, the radiative efficiency, has been inferred to be 10\%, in agreement
with expectations from thin disk accretion models. But the existence of billion
solar-mass SMBHs powering quasars at $z > 7$ challenges this picture: provided
they respect the Eddington limit, there is not enough time to grow $z>7$ SMBHs
from stellar remnant seeds unless the radiative efficiency is below 10\%. Here
we show that one can constrain the radiative efficiencies of the most distant
quasars known using foreground neutral intergalactic gas as a
cosmological-scale ionizing photon counter. From the Ly$\alpha$ absorption
profiles of ULAS J1120+0641 ($z=7.09$) and ULAS J1342+0928 ($z=7.54$), we
determine posterior median radiative efficiencies of 0.08\% and 0.1\%,
respectively, and the combination of the two measurements rule out the
canonical 10\% efficiency at 99.8\% credibility after marginalizing over the
unknown obscured fraction. This low radiative efficiency implies rapid mass
accretion for the earliest SMBHs, greatly easing the tension between the age of
the Universe and the SMBH masses. However, our measured efficiency may instead
reflect nearly complete obscuration by dusty gas in the quasar host galaxies
over the vast majority of their SMBH growth. Assuming 10\% efficiency during
unobscured phases, we find that the obscured fraction would be $>82\%$ at 95\%
credibility, and imply a $25.7^{+49.6}_{-16.5}$ times larger obscured than
unobscured luminous quasar population at $z>7$.
