Quantum Simulation of Light-Front QCD for Jet Quenching in Nuclear Environments

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.Comment: 56 pages, 9 figures; v2: add a section on the simulation of the LPM effect in gluon radiation; v3: added more discussions in introduction, modified discussions of simulation result