Classification using variational quantum circuits is a promising frontier in quantum machine learning. Quantum supervised learning (QSL) applied to classical data using variational quantum circuits involves embedding the data into a quantum Hilbert space and optimizing the circuit parameters to train the measurement process. In this context, the efficacy of QSL is inherently influenced by the selection of quantum embedding. In this study, a classical‐quantum hybrid approach is introduced for optimizing quantum embedding beyond the limitations of the standard circuit model of quantum computation (i.e., completely positive and trace‐preserving maps) for general multi‐channel data. The performance of various models is benchmarked in this framework using the CIFAR‐10 and Tiny ImageNet datasets and provide theoretical analyses that guide model design and optimization.