  We develop a framework to simulate jet quenching in nuclear environments on a
quantum computer. The formulation is based on the light-front Hamiltonian
dynamics of QCD. The Hamiltonian consists of three parts relevant for jet
quenching studies: kinetic, diffusion and splitting terms. In the basis made up
of $n$-particle states in momentum space, the kinetic Hamiltonian is diagonal.
Matrices representing the diffusion and splitting parts are sparse. The
diffusion part of the Hamiltonian depends on classical background gauge fields,
which need to be sampled classically before constructing quantum circuits for
the time evolution. The cost of the sampling scales linearly with the time
length of the evolution and the momentum grid volume. The framework
automatically keeps track of quantum interference and thus it can be applied to
study the Landau-Pomeranchuk-Migdal effect in cases with more than two coherent
splittings, which is beyond the scope of state-of-the-art analyses, no matter
whether the medium is static or expanding, thin or thick, hot or cold. We apply
this framework to study a toy model and gluon in-medium radiation on a small
lattice. The essence of the Landau-Pomeranchuk-Migdal effect is observed in the
quantum simulation results of both the toy model and the gluon case, which is
quantum decoherence caused by medium interactions that suppresses the total
radiation probability.
