  The faint-end slope of the quasar luminosity function at z~6 and its
implication on the role of quasars in reionizing the intergalactic medium at
early times has been an outstanding problem for some time. The identification
of faint high-redshift quasars with luminosities of <1e44.5 erg/s is
challenging. They are rare (few per square-degree) and the separation of these
unresolved quasars from late-type stars and compact star-forming galaxies is
difficult from ground-based observations alone. In addition, source confusion
becomes significant at >25mag, with 30% of sources having their flux
contaminated by foreground objects when the seeing resolution is ~0.7". We
mitigate these issues by performing a pixel-level joint processing of ground
and space-based data from Subaru/HSC and HST/ACS. We create a deconfused
catalog over the 1.64 square-degrees of the COSMOS field, after accounting for
spatial varying PSFs and astrometric differences between the two datasets. We
identify twelve low-luminosity (M_UV ~ -21 mag) z>6 quasar candidates through
(i) their red color measured between ACS/F814W and HSC/i-band and (ii) their
compactness in the space-based data. Non-detections of our candidates in Hubble
DASH data argues against contamination from late-type stars. Our constraints on
the faint end of the quasar luminosity function at z~6.4 suggests a negligibly
small contribution to reionization compared to the star-forming galaxy
population. The confirmation of our candidates and the evolution of number
density with redshift could provide better insights into how supermassive
galaxies grew in the first billion years of cosmic time.
