Optimal control of spins by Analytical Lie Algebraic Derivatives

Computation of derivatives (gradient and Hessian) a fidelity function is one the most crucial steps in many optimization algorithms. Having access to accurate methods for computing these even more desirable where process requires propagation computations over steps, which particularly important optimal control spin systems. Here we propose novel numerical approach, ESCALADE (Efficient Spin Control using Analytical Lie Algebraic Derivatives), that offers exact first second by taking advantage properties group 2 × unitary matrices, SU(2), its algebra, algebra skew-Hermitian su(2). A full mathematical treatment proposed method along with some examples are presented.