  Jet quenching, the modification of the properties of a QCD jet when the
parton cascade takes place inside a medium, is an intrinsically quantum
process, where color coherence effects play an essential role. Despite a very
significant progress in the last years, the simulation of a full quantum medium
induced cascade remains inaccessible to classical Monte Carlo parton showers.
In this situation, alternative formulations are worth being tried and the fast
developments in quantum computing provide a very promising direction. The goal
of this paper is to introduce a strategy to quantum simulate single particle
momentum broadening, the simplest building block of jet quenching. Momentum
broadening is the modification of the quark or gluon transverse momentum due
interactions with the underlying medium, modeled as a QCD background field. At
the lowest order in $\alpha_s$ that we consider here, momentum broadening does
not involve parton splittings and particle number is conserved, greatly
simplifying the quantum algorithmic implementation. This quantity is, however,
very relevant for the phenomenology of RHIC, LHC or the future EIC.
