Riemannian optimizer for phase estimation of LPD architectures

Implementation of a global Riemannian optimization algorithm for geodesic distance minimization in the manifold SU(N) to estimate the LPD architecture phase masks that factorize any given target matrix. First, we run a Newton-CG (conjugate gradient descent) minimizer over a sample of random, uniformly distributed, initial phases, and select the smallest ``local minima'' found. Subsequently, we execute an adaptive Newton-Raphson method to improve on the precision of the chosen solution. In both cases the exact gradient is provided to the algorithm, along with a finite-difference estimator of the Hessian using such analytical information.