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.