  The statistics of galactic-scale quasar pairs can elucidate our understanding
of the dynamical evolution of supermassive black hole (SMBH) pairs, the duty
cycles of quasar activity in mergers, or even the nature of dark matter, but
have been challenging to measure at cosmic noon, the prime epoch of massive
galaxy and SMBH formation. Here we measure a double quasar fraction of $\sim
6.2\pm0.5\times 10^{-4}$ integrated over $\sim 0.3-3$ arcsec separations
(projected physical separations of $\sim 3-30\,{\rm kpc}$ at $z\sim 2$) in
luminous ($L_{\rm bol}>10^{45.8}\,{\rm erg\,s^{-1}}$) unobscured quasars at
$1.5<z<3.5$, using Gaia EDR3-resolved pairs around SDSS DR16 quasars. The
measurement was based on a sample of 60 Gaia-resolved double quasars (out of
487 Gaia pairs dominated by quasar+star superpositions) at these separations,
corrected for pair completeness in Gaia, which we quantify as functions of pair
separation, magnitude of the primary, and magnitude contrast. The double quasar
fraction increases towards smaller separations by a factor of $\sim 5$ over
these scales. The division between physical quasar pairs and lensed quasars in
our sample is currently unknown, requiring dedicated follow-up observations (in
particular, deep, sub-arcsec-resolution IR imaging for the closest pairs).
Intriguingly, at this point the observed pair statistics are in rough agreement
with theoretical predictions both for the lensed quasar population in mock
catalogs and for dual quasars in cosmological hydrodynamic simulations.
Upcoming wide-field imaging/spectroscopic space missions such as Euclid, CSST
and Roman, combined with targeted follow-up observations, will conclusively
measure the abundances and host galaxy properties of galactic-scale quasar
pairs, offset AGNs, and sub-arcsec lensed quasars across cosmic time.
