  Quantum computing provides a promising approach for solving the real-time
dynamics of systems consist of quarks and gluons from first-principle
calculations that are intractable with classical computers. In this work, we
start with an initial problem of the ultra-relativistic quark-nucleus
scattering and present an efficient and precise approach to quantum simulate
the dynamics on the light front. This approach employs the eigenbasis of the
asymptotic scattering system and implements the compact scheme for basis
encoding. It exploits the operator structure of the light-front Hamiltonian of
the scattering system, which enables the Hamiltonian input scheme that utilizes
the quantum Fourier transform for efficiency. It utilizes the truncated Taylor
series for the dynamics simulations. The qubit cost of our approach scales
logarithmically with the Hilbert space dimension of the scattering system. The
gate cost has optimal scaling with the simulation error and near optimal
scaling with the simulation time. These scalings make our approach advantageous
for large-scale dynamics simulations on future fault-tolerant quantum
computers. We demonstrate our approach with a simple scattering problem and
benchmark the results with those from the Trotter algorithm and the classical
calculations, where good agreement between the results is found.
