Abstract:
Quantum neural networks (QNNs) are gaining attention as versatile models for quantum machine learning, but training them effectively remains a challenge. Most existing approaches, such as quantum multilayer perceptrons, use fidelity-based cost functions. While well-suited for pure states, these measures are less reliable when inputs and outputs are mixed states—a situation common in learning quantum channels. In this work, we introduce a training framework built on a relative entropy-inspired cost function. By quantifying the directional divergence between learned and target states, relative entropy provides a more informative and principled measure than linear fidelity, naturally capturing both spectral and eigenvector differences in mixed states. This approach preserves the completely positive structure of the network, supports efficient backpropagation in layered QNN configurations, and achieves improved accuracy and convergence over fidelity-based training. These results highlight entropy-based optimization as a promising path toward scalable, robust, and noise-resilient quantum learning.