  Sachdev-Ye-Kitaev (SYK) model has emerged as a new paradigm of the
non-Fermi-liquid behavior. Here we investigate a possibility of having a
superconducting off-diagonal long-range order (ODLRO) and a pseudogap phase
within the SYK framework. We found that ODLRO may be established in spin-1/2
version of the model with the time-reversal invariance and an extra attractive
interaction. If the latter is taken as the on-site negative-$U$ Hubbard term,
it leads to the pseudogap phase at $U<U_c$ dominated by quantum fluctuations of
local phases. These fluctuations are described by a quantum version of the
Kuramoto model, traditionally employed to illustrate synchronization of
classical non-linear oscillators. In the opposite limit of large $U$, the
SYK+Hubbard model is approaching a certain generalization of the integrable
Richardson model. We present exact diagonalization studies, along with analytic
solutions of the aforementioned limiting cases. We also discuss possible
holographic interpretations of the model, ODLRO and the pseudogap.
