  To describe the chiral magnetic effect, the chiral chemical potential $\mu_5$
is introduced to imitate the impact of topological charge changing transitions
in the quark-gluon plasma under the influence of an external magnetic field. We
employ the (1+1) dimensional Nambu-Jona-Lasinio (NJL) model to study the chiral
phase structure and chirality charge density of strongly interacting matter
with finite chiral chemical potential $\mu_5$ in a quantum simulator. By
performing the Quantum imaginary time evolution (QITE) algorithm, we simulate
the (1+1) dimensional NJL model on the lattice at various temperature $T$ and
chemical potentials $\mu$, $\mu_5$ and find that the quantum simulations are in
good agreement with analytical calculations as well as exact diagonalization of
the lattice Hamiltonian.
