  We present a quantum algorithm based on the Tensor-Train Thermo-Field
Dynamics (TT-TFD) method to simulate the open quantum system dynamics of
intramolecular charge transfer modulated by an optical cavity on noisy
intermediate-scale quantum (NISQ) computers. We apply our methodology to a
model that describes the $\pi\pi^*$ to CT1 intermolecular charge transfer
within the carotenoid-porphyrin-C60 molecular triad solvated in tetrahydrofuran
(THF) and placed inside an optical cavity. We find how the dynamics is
influenced by the cavity resonance frequency and strength of the light-matter
interaction, showcasing the NISQ-based simulations to capture these effects.
Furthermore, we compare the approximate predictions of Fermi's Golden Rule
(FGR) rate theory and Ring-Polymer Molecular Dynamics (RPMD) to numerically
exact calculations, showing the capabilitis of quantum computing methods to
assess the limitations of approximate methods.
