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 with respect to the tomography result. Convex optimization, widely used in machine learning, is able to generate a global optimum 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. Here, we reconstruct the seawater channel using convex optimization and further test it on the seven fundamental gates. We compare our method to the standard-inversion and norm-optimization approaches using the cost function value and our proposed state deviation. The advantages convince that our method enables a more precise and robust estimation of the elements of the process matrix with less demands on preliminary resources. In addition, we examine on a set of non-unitary channels and the reconstructions reach up to $99.5\%$ accuracy. Our method offers a more universal tool for further analyses on the components of the quantum channels and we believe that the crossover between quantum process tomography and convex optimization may help us move forward to machine learning of quantum channels.

量子过程层析成像通常用于完全表征未知的量子过程。然而，它可能导致非物理过程矩阵，这将导致关于层析成像结果的信息丢失。广泛用于机器学习的凸优化能够生成最适合原始数据的全局最优值，同时将过程层析成像保持在合法区域。只有正确揭示过程的原始作用，我们才能更深入地探究其相变和哈密顿量等性质。在这里，我们使用凸优化重建海水通道，并在七个基本门上进一步测试。我们使用成本函数值和我们提出的状态偏差将我们的方法与标准反转和规范优化方法进行比较。这些优势使我们相信我们的方法能够对过程矩阵的元素进行更精确和稳健的估计，同时对初始资源的需求更少。此外，我们检查了一组非单一通道，重建达到$99.5\%$准确性。我们的方法为进一步分析量子通道的成分提供了一个更通用的工具，我们相信量子过程层析成像和凸优化之间的交叉可以帮助我们推进量子通道的机器学习。