  The leading order $\alpha_s$ effect in jet quenching corresponds to the
broadening of the jet's transverse momentum, due to the multiple interactions
with the underlying medium. A complete understanding of momentum broadening is
critical for the success of jet quenching phenomenology.
  In this talk, we introduce a strategy to quantum simulate single particle
momentum broadening in a QCD background medium. We argue that it is, in
principle, possible to extract the jet quenching parameter $\hat{q}$ from such
an algorithm. More importantly, this corresponds to the first step towards
simulating full medium induced parton showers, which is far beyond the
capabilities of classical computers.
