Projection-operator-based Newton method for the trajectory optimization of closed quantum systems

Quantum optimal control is an important technology that enables fast state preparation and gate design. In the absence of analytic solution, most quantum methods rely on iterative scheme to update solution estimate. At present, convergence rate existing solvers is, at most, superlinear. This paper develops a general-purpose solver for based projection operator Newton method trajectory optimization, or PRONTO. Specifically, proposed approach uses incorporate Schr\"odinger equation directly into cost function, which then minimized using Newton's descent method. each iteration, direction obtained by computing linear-quadratic trajectory-optimization problem. The resulting guarantees monotonic every iteration quadratic in proximity solution. potential PRONTO showcased solving state-to-state mapping problem qubit providing comparisons state-of-the-art