Newton algorithm for Hamiltonian characterization in quantum control

TL;DR

This paper introduces a Newton-based algorithm utilizing continuation methods to accurately determine the Hamiltonian of quantum systems from known evolution operators, demonstrated on two-level and molecular systems.

Contribution

It presents a novel Newton algorithm with a continuation approach for Hamiltonian identification in quantum control, improving convergence and accuracy.

Findings

Accurate Hamiltonian estimates achieved in some cases.

Algorithm's convergence depends on basin of attraction and solution uniqueness.

Numerical limits identified for the proposed method.

Abstract

We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank-Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown parameters are obtained in some cases. We discuss the numerical limits of the algorithm in terms of basin of convergence and non uniqueness of the solution.