Quantum Comb Tomography via Learning Isometries on Stiefel Manifold

Explicit mathematical reconstructions of quantum combs play a significant role in developing quantum information science. However, tremendous parameter requirements and physical constraint implementations have become computationally nonignorable encumbrances. In this Letter, we propose an efficient method for quantum comb tomography by learning isometries on the Stiefel manifold via 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 comb while processing the tomography. Remarkably, this method enables the dimension-reduced quantum comb tomography by reducing the ancillary dimensions of isometries with bounded error. As a result, our proposed method exhibits high accuracy and efficiency.