An optimized greedy reconstruction algorithm for dipole momentum operators

Abstract

In a previous work (Salomon 2009), an algorithm was proposed to compute a family of selective controls that enables the efficient Hamiltonian identification of quantum systems. These controls are iteratively computed for a given set of linearly independent matrices, whose span form the space where the unknown Hamiltonian is sought. In this paper, we show by direct numerical experiments that the procedure presented in (Salomon 2009) can suffer from a lack of robustness. This is due to the high non-linearity of the problem generated by the bilinear state-control structure and to the fact that the final results strongly depend on the basis matrices chosen before running the algorithm. For this reason, a randomly chosen set of linear independent matrices does not necessarily lead to a set of robust selective fields that allows an accurate identification of the unknown Hamiltonian. To tackle this problem we propose a new optimized version of this algorithm. This new strategy consists in extending the greedy character of the original algorithm in a way that more matrices, not necessarily linearly independent, are tested in a parallelizable fashion. A simple criterion is then used to identify which matrix has to be chosen at each iteration among the tested ones in order to produce the new selective field. Therefore, the new proposed algorithm is capable to choose the set of needed basis matrices and their corresponding order. This strategy leads to the generation of selective fields that guarantee more robustness in the numerical identification of the Hamiltonian. Results of numerical experiments demonstrate the effectiveness of the new proposed algorithm.