  In this work, we investigate the capability of known quantum-computing
algorithms for fault-tolerant quantum computing to simulate the laser-driven
electron dynamics in small molecules such as lithium hydride. These
computations are executed on a quantum-computer simulator. Results are compared
with the time-dependent full configuration interaction method (TD-FCI). The
actual wave packet propagation is closely reproduced using the Jordan-Wigner
transformation and the Trotter product formula. In addition, the time-dependent
dipole moment, as an example of a time-dependent expectation value, is
calculated using the Hadamard test. In order to include non-Hermitian operators
in the dynamics, a similar approach to the quantum imaginary time evolution
(QITE) algorithm is employed to translate the propagator into quantum gates.
Thus, ionization of a hydrogen molecule under the influence of a complex
absorbing potential can be simulated accurately. All quantum computer
algorithms used scale polynomially rather than exponentially as TD-FCI and
therefore hold promise for substantial progress in the understanding of
electron dynamics of increasingly large molecular systems in the future.
