Reconstruction of the Real Quantum Channel via Convex Optimization

TL;DR

This paper demonstrates how convex optimization can be used to accurately reconstruct physical quantum channels from experimental data, ensuring valid process matrices and enabling deeper analysis of quantum properties.

Contribution

It introduces a convex optimization-based method for reconstructing physical quantum channels from experimental data, addressing issues of unphysical process matrices in traditional tomography.

Findings

Successfully reconstructed quantum channel from seawater experiment

Proposed a state deviation criterion for process fit evaluation

Showed potential for integrating quantum tomography with machine learning

Abstract

Quantum process tomography is often used to completely characterize an unknown quantum process. However, it may lead to an unphysical process matrix, which will cause the loss of information respect to the tomography result. Convex optimization, widely used in machine learning, is able to generate a global optimal model that best fits the raw data while keeping the process tomography in a legitimate region. Only by correctly revealing the original action of the process can we seek deeper into its properties like its phase transition and its Hamiltonian. Thus, we reconstruct the real quantum channel using convex optimization from our experimental result obtained in free-space seawater. In addition, we also put forward a criteria, state deviation, to evaluate how well the reconstructed process fits the tomography result. We believe that the crossover between quantum process tomography and convex optimization may help us move forward to machine learning of quantum channels.