  Nucleus is a typical many-body quantum system. Full calculation of a nuclear
system in a classical computer is far beyond the capacity of current classical
computers. With fast development of hardware, the prospect of using quantum
computers in nuclear physics is closing. Here, we report a full quantum
package, QCSH, for solving nuclear shell-model in a quantum computer. QCSH uses
the linear combination of unitaries formalism of quantum computing, and
performs all calculations in a quantum computer. The complexities of qubit
resource, number of basic gates of QCSH, are both polynomial to the nuclear
size. QCSH can already provide meaningful results in the near term. As
examples, the binding energies of twelve light nuclei, $^{2}$H, $^{3}$H,
$^{3}$He, $^{4}$He, $^{6}$Li, $^{7}$Li, $^{12}$C, $^{14}$N, $^{16}$O, $^{17}$O,
$^{23}$Na and $^{40}$Ca are calculated using QCSH in a classical quantum
emulator. The binding energy of Deuteron has already been experimentally
studied using QCSH on a superconducting quantum computing device. QCSH not only
works in near-term quantum devices, but also in future large-scale quantum
computers. With the development of quantum devices, nuclear system constitutes
another promising area for demonstrating practical quantum advantage.
