Solving coupled Non-linear Schr\"{o}dinger Equations via Quantum Imaginary Time Evolution

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.