  In recent years, researchers have been exploring the applications of noisy
intermediate-scale quantum (NISQ) computation in various fields. One important
area in which quantum computation can outperform classical computers is the
ground state problem of a many-body system, e.g., the nucleus. However, using a
quantum computer in the NISQ era to solve a meaningful-scale system remains a
challenge.
  To calculate the ground energy of nuclear systems, we propose a new algorithm
that combines classical shadow and subspace diagonalization techniques. Our
subspace is composed of matrices, with the basis of the subspace being the
classical shadow of the quantum state. We test our algorithm on nuclei
described by Cohen-Kurath shell model and USD shell model. We find that the
accuracy of the results improves as the number of shots increases, following
the Heisenberg scaling.
