Control over the training performance of quantum state tomography with reservoir computing networks

The evaluation of unknown states for a given quantum system is one of the key problems in quantum information processing. The most efficient method of state characterization is quantum state tomography (QST), where the full-density matrices are reconstructed from the experimental measurements or numerical simulations performed on quantum states. The improvement of the computational performance in quantum state tomography and its related problems is a challenging task for modern theoretical physics. The general scheme of computing deals with the input information that goes into a quantum reservoir through a recurrent evolution. After the evolution, the final output is obtained as the linear combination of the readout elements. In our approach, the quantum reservoir is modeled with the Lindbladian equation. The control over performance is made by the coherent coupling parameter between the input quantum state and the reservoir. The control feedback algorithm is represented with the set of Kolesnikov’s target attractor algorithm to drive certain parameters of quantum state tomography, particularly, the outputs for the density matrix. Here we formulate the target attractor feedback in a discrete form to improve the training performance of QST and then develop a basic example of the state tomography for the quantum system of spin 1/2. We conclude by mentioning the basic features of our algorithm and its possible development.