  Coupled non-linear Schr\"{o}dinger equations are crucial in describing
dynamics of many particle systems. We present a quantum imaginary time
evolution (ITE) algorithm as a solution to such equations in the case of
nuclear Hartree-Fock equations. Under a simplified Skyrme interaction model, we
calculate the ground state energy of an oxygen-16 nucleus and demonstrate that
the result is in agreement with the classical ITE algorithm.
