  We consider fallback accretion after an ultra-stripped supernova (USSN) that
accompanies formation of a binary neutron star (BNS) or a neutron star-black
hole binary (NS-BH). The fallback matter initially accretes directly to the
nascent NS, while it starts to accrete to the circumbinary disk, typically
$0.1\mbox{-}1\, \mathrm{day}$ after the onset of the USSN explosion. The
circumbinary disk mass further accretes, forming mini disks around each compact
object, with a super-Eddington rate up to a few years. We show that such a
system constitutes a binary ultraluminous X-ray source (ULX), and a fraction of
the X rays can emerge through the USSN ejecta. We encourage follow-up
observations of USSNe within $\lesssim 100\,\rm Mpc$ and $\sim
100\mbox{-}1,000\,\mathrm{day}$ after the explosion using Chandra, XMM Newton
and NuSTAR, which could detect the X-ray counterpart with time variations
representing the properties of the nascent compact binary, e.g., the orbital
motion of the binary, the spin of the NS, and/or the quasiperiodic oscillation
of the mini disks.
