  We present the first direct and non-perturbative computation of the graviton
spectral function in quantum gravity. This is achieved with the help of a novel
Lorentzian renormalisation group approach, combined with a spectral
representation of correlation functions. We find a positive graviton spectral
function, showing a massless one-graviton peak and a multi-graviton continuum
with an asymptotically safe scaling for large spectral values. We also study
the impact of a cosmological constant. Further steps to investigate scattering
processes and unitarity in asymptotically safe quantum gravity are indicated.
