This is the case with a caveat: It only works for a weak linearized theory. If gravitons are a small field perturbation on a flat background in a linear <PERSON> field equation this is the case. In greater generality this is less certain. Energy is not localizable in general relativity. So what I am about to outline below is a linear quantum gravity for long wavelength gravitons in the IR limit.
A gravity wave is a perturbation on a background metric $\eta_{ab}$ with the total metric $$ g_{ab}~=~\eta_{ab}~+~h_{ab}. $$ The flat background metric has zero Ricci curvature so that to first order in the perturbation expansion $$ R_{ab}~=~\delta R_{ab}, $$ which enters into the <PERSON> field equation $R_{ab}~-~1/2Rg_{ab}~=~\kappa T_{ab}$, where $\kappa~=~8\pi G/c^4$ is the very small coupling constant between the momentum-energy source and the spacetime configuration or field. The Ricci curvature to first order is then $$ R_{ab}~=~{1\over 2}\Big(\partial_c\partial_a{h^c}b~+~\partial_c\partial_b{h^c}_a~-~\partial_a\partial_bh~-~\partial_c\partial^ch{ab}\Big). 651
$$ To within first order the harmonic gauge $\partial_c{h^c}a~=~1/2\partial_mu h$ the <PERSON> field equation gives $$ \partial^c\partial_ch{ab}~-~\frac{1}{2}\eta_{ab}\partial^c\partial_ch~=~{{16\pi G}\over c^4}T_{ab}, $$ which is well defined for the traceless metric term ${\bar h}{ab}~=~h{ab}~-~{1\over 2}\eta_{ab}h$ with the simple wave equation $$ \partial^c\partial_c{\bar h}{ab}~=~{{16\pi G}\over c^4}T{ab}. $$
For the wave in vacuum the momentum energy source is set to zero, and the wave equation is $\partial^c\partial_c{\bar h}{ab}~=~0$. This is a bi-vector analogue to the simple wave equation for an electromagnetic wave in free space. The wave is a transverse traceless wave $h{ab}~=~A^{TT}{ab}exp(ik_cx^c)$ with $$ A^{TT}{ab}~=~\left(\matrix{0 & 0 & 0 & 0\cr 0 & A_{xx} & A_{yx} & 0\cr 0 & A_{xy} & -A_{xx} & 0\cr 0 & 0 & 0 & 0 }\right). $$ The terms $A_{xx}$ and $A_{xy}$ represent a polarization direction. The linearized gravity wave then has a helicity of two, which has its quantum analogue in the di-photon state in quantum optics.
The analogue with a photon in this linearized approximation is for the metric perturbation $h_{ab}~=~\phi^c_a\phi_{bc}$ expanded according to a field. To take this forwards let us expand the field $\phi^a_b$ according to harmonic oscillator operators $b,~b^\dagger$. The fields are then expanded as $$ \phi^a_b~=~\frac{1}{\sqrt{2}}\sum_k E^a_b (b(k)e^{i\theta(k)} + b^\dagger e^{-i\theta(k)}) $$ where $E^a_b$ tetrad, which is discussed more below. 526