Solving coupled non-linear schrödinger equations via quantum imaginary time evolution

Coupled non-linear Schrödinger 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 approach. 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. We examine bottlenecks and deficiencies in the quantum algorithm and suggest possible improvements.