  In this study, we explore the real-time dynamics of the chiral magnetic
effect (CME) at a finite temperature in the (1+1)-dimensional QED, the massive
Schwinger model. By introducing a chiral chemical potential $\mu_5$ through a
quench process, we drive the system out of equilibrium and analyze the induced
vector currents and their evolution over time. The Hamiltonian is modified to
include the time-dependent chiral chemical potential, thus allowing the
investigation of the CME within a quantum computing framework. We employ the
quantum imaginary time evolution (QITE) algorithm to study the thermal states,
and utilize the Suzuki-Trotter decomposition for the real-time evolution. This
study provides insights into the quantum simulation capabilities for modeling
the CME and offers a pathway for studying chiral dynamics in low-dimensional
quantum field theories.
