  Jets provide one of the primary probes of the quark-gluon plasma produced in
ultrarelativistic heavy ion collisions and the cold nuclear matter explored in
deep inelastic scattering experiments. However, despite important developments
in the last years, a description of the real-time evolution of QCD jets inside
a medium is still far from complete. In our previous work, we have explored
quantum technologies as a promising alternative theoretical laboratory to
simulate jet evolution in QCD matter, to overcome inherent technical
difficulties in present calculations. Here, we extend our previous
investigation from the single particle to the multiple particle Fock spaces,
taking into account gluon production. Based on the light-front Hamiltonian
formalism, we construct a digital quantum circuit that tracks the evolution of
a multi-particle jet probe in the presence of a stochastic color background.
Using the quantum simulation algorithm, we show the medium-induced modification
to the jet evolution in both the momentum broadening and gluon production.
