  We demonstrate fully crystalline, single-mode ultrahigh quality factor
integrated microresonators comprising epitaxially grown Si$_{0.86}$Ge$_{0.14}$
waveguide cores with silicon claddings. These waveguides support resonances
with internal $Q >10^8$ for both polarization modes, a nearly
order-of-magnitude improvement over that seen in prior integrated Si photonics
platforms. The maximum $Q$ is $1.71\pm0.06 \times 10^8$ for the transverse
magnetic (TM) polarization mode, corresponding to a loss of $0.39\pm0.02$ dB/m.
Together with silicon's strong Kerr nonlinearity and low losses in the optical,
microwave and acoustic regimes, our results could lead to the
Si$_{1-x}$Ge$_x$/Si architecture unlocking important new avenues for Kerr
frequency combs, optomechanics, and quantum transduction.
