  We present an investigation of the quiescent and transient X-ray binaries
(XRBs) of the Galactic Center (GC). We extended our Chandra analysis of the
non-thermal X-ray sources, located in the central parsec, from Hailey et al.
(2018), using an additional 4.6 Msec of ACIS-S data obtained in 2012-2018. The
individual Chandra spectra of the 12 sources fit to an absorbed power-law model
with a mean photon index $\Gamma$~2 and show no Fe emission lines. Long-term
variability was detected from nine of them, confirming that a majority are
quiescent XRBs. Frequent X-ray monitoring of the GC revealed that the 12
non-thermal X-ray sources, as well as four X-ray transients have shown at most
a single outburst over the last two decades. They are distinct from the six
known neutron star LMXBs in the GC, which have all undergone multiple outbursts
with <~ 5 year recurrence time on average. Based on the outburst history data
of the broader population of X-ray transients, we conclude that the 16 sources
represent a population of ~240-630 tightly-bound BH-LMXBs with ~4-12 hour
orbital periods, consistent with the stellar/binary dynamics modelling in the
vicinity of Sgr A*. The distribution of the 16 BH-LMXB candidates is disk-like
(at 87% CL) and aligned with the nuclear star cluster. Our results have
implications for XRB formation and the rate of gravitational wave events in
other galactic nuclei.
