  We derive some of the central equations governing quantum fluctuations in
gravitational waves, making use of general relativity as a sensible effective
quantum theory at large distances. We begin with a review of classical
gravitational waves in general relativity, including the energy in each mode.
We then form the quantum ground state and coherent state, before then obtaining
an explicit class of squeezed states. Since existing gravitational wave
detections arise from merging black holes, and since the quantum nature of
black holes remains puzzling, one can be open-minded to the possibility that
the wave is in an interesting quantum mechanical state, such as a highly
squeezed state. We compute the time and space two-point correlation functions
for the quantized metric perturbations. We then constrain its amplitude with
LIGO-Virgo observations. Using existing LIGO-Virgo data, we place a bound on
the (exponential) squeezing parameter of the quantum gravitational wave state
of $\zeta < 41$.
