Designing multi-qubit quantum logic gates with experimental constraints is an important problem in quantum computing. In this talk, I will introduce a new quantum optimal control algorithm for finding unitary transformations with constraints on the Hamiltonian. The algorithm, geodesic pulse engineering (GEOPE), uses differential programming and geodesics on the Riemannian manifold of SU(2^n) for n qubits. Instead of local gradient descent, the parameter updates of GEOPE are designed to follow the geodesic to the target unitary as closely as possible. In our recent paper, we show, both numerically and with analytical evidence, that our algorithm converges significantly faster than the widely used gradient-based method GRAPE, where we find solutions that are not accessible to GRAPE in a reasonable amount of time. The strength of the method is illustrated with varied multi-qubit gates in 2D neutral Rydberg atom platforms.