Unitary quantum process tomography by time-delayed measurements

The unitary dynamics of a quantum system implicitly defines its characterizing Hamiltonian. However, quantum process tomography methods are resource intensive in general. In this work, we investigate an approach based on the Takens and Ruelle time-delay embedding to learn the Hamiltonian from quantum measurements. By minimizing the Kullback-Leibler divergence between the experimental probabilities and the output of a model ansatz, we achieve convergence to the true Hamiltonian for toy model problems. Furthermore, a model parametrization inspired by the topology of the target system could help avoid local minima during learning and reduce the amount of required samples.