  We study the hardness of learning unitary transformations in $U(d)$ via
gradient descent on time parameters of alternating operator sequences. We
provide numerical evidence that, despite the non-convex nature of the loss
landscape, gradient descent always converges to the target unitary when the
sequence contains $d^2$ or more parameters. Rates of convergence indicate a
"computational phase transition." With less than $d^2$ parameters, gradient
descent converges to a sub-optimal solution, whereas with more than $d^2$
parameters, gradient descent converges exponentially to an optimal solution.
