  We explore quantum phase transitions using two probes of quantum chaos:
out-of-time-order correlators (OTOCs) and the $r$-parameter obtained from the
level spacing statistics. In particular, we address $p$-spin models associated
with quantum annealing or reverse annealing. Quantum annealing triggers
first-order or second-order phase transitions, which is crucial for the
performance of quantum devices. We find that the time-averaging OTOCs for the
ground state and the average $r$-parameter change behavior around the
corresponding transition points, diagnosing the phase transition. Furthermore,
they can identify the order (first or second) of the phase transition by their
behavior at the quantum transition point, which changes abruptly (smoothly) in
the case of first-order (second-order) phase transitions.
