  Nuclear physics, whose underling theory is described by quantum gauge field
coupled with matter, is fundamentally important and yet is formidably challenge
for simulation with classical computers. Quantum computing provides a perhaps
transformative approach for studying and understanding nuclear physics. With
rapid scaling-up of quantum processors as well as advances on quantum
algorithms, the digital quantum simulation approach for simulating quantum
gauge fields and nuclear physics has gained lots of attentions. In this review,
we aim to summarize recent efforts on solving nuclear physics with quantum
computers. We first discuss a formulation of nuclear physics in the language of
quantum computing. In particular, we review how quantum gauge fields~(both
Abelian and non-Abelian) and its coupling to matter field can be mapped and
studied on a quantum computer. We then introduce related quantum algorithms for
solving static properties and real-time evolution for quantum systems, and show
their applications for a broad range of problems in nuclear physics, including
simulation of lattice gauge field, solving nucleon and nuclear structure,
quantum advantage for simulating scattering in quantum field theory,
non-equilibrium dynamics, and so on. Finally, a short outlook on future work is
given.
