  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.
