Quantum Network Tomography via Learning Isometries on Stiefel Manifold

Explicit mathematical reconstructions of quantum networks play a significant role in developing quantum information science. However, tremendous parameter requirements and physical constraint implementations have become computationally non-ignorable encumbrances. In this work, we propose an efficient method for quantum network tomography by learning isometries on the Stiefel manifold. Tasks of reconstructing quantum networks are tackled by solving a series of unconstrained optimization problems with significantly fewer parameters. The stepwise isometry estimation shows the capability for providing information of the truncated quantum network while processing the tomography. Remarkably, this method enables the dimension-reduced quantum network tomography by reducing the ancillary dimensions of isometries with bounded error. As a result, our proposed method exhibits high accuracy and efficiency.