  Einstein's general relativity, as the most successful theory of gravity, is
one of the cornerstones of modern physics. However, the experimental tests for
gravity in the high energy region are limited. The emerging gravitational-wave
astronomy has opened an avenue for probing the fundamental properties of
gravity in strong and dynamical field, and in particular, high energy regime.
In this work, we test the parity conservation of gravity with gravitational
waves. If the parity symmetry is broken, the left- and right-handed modes of
gravitational waves would follow different equations of motion, dubbed as
birefringence. We perform full Bayesian inference by comparing the
state-of-the-art waveform with parity violation with the compact binary
coalescence data released by LIGO and Virgo collaboration. We do not find any
violations of general relativity, thus constrain the lower bound of the
parity-violating energy scale to be $0.09$ GeV through the velocity
birefringence of gravitational waves. This provides the most stringent
experimental test of gravitational parity symmetry up to date. We also find
third generation gravitational-wave detectors can enhance this bound to
$\mathcal{O}(10^2)$ GeV if there is still no violation, comparable to the
current LHC energy scale in particle physics, which indicates
gravitational-wave astronomy can usher in a new era of testing the ultraviolet
behavior of gravity in the high energy region.
