Quantum Optimal Control with Geodesic Pulse Engineering

Designing multi-qubit quantum logic gates with experimental constraints is an important problem in quantum computing. Here, we develop 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 $\textrm{SU}(2^n)$ for $n$ qubits. We demonstrate significant improvements over the widely used gradient-based method, GRAPE, for designing multi-qubit quantum gates. Instead of a local gradient descent, the parameter updates of GEOPE are designed to follow the geodesic to the target unitary as closely as possible. We present numerical results that show that our algorithm converges significantly faster than GRAPE for a range of gates and can find solutions that are not accessible to GRAPE in a reasonable amount of time. The strength of the method is illustrtated with varied multi-qubit gates in 2D neutral Rydberg atom platforms.