Post-Selection-Free Quantum Automated Learning

Quantum automated learning (QAL) trains quantum models by directly updating quantum states, offering an approach to quantum machine learning that avoids optimizing variational circuit parameters. However, post-selection constrains the probability of obtaining the final learned model. We develop a post-selection-free QAL algorithm that organizes a complete training path into a coherent quantum circuit and uses fixed-point amplitude amplification to increase the probability of obtaining the learned model. We provide theoretical guarantees on output error and learning loss, and identify conditions under which additional coherent resources reduce the cost of restarting failed trajectories. The construction gives QAL a coherent implementation with explicit learning guarantees and resource costs, enabling a model with certified learning quality and controlled output error to be obtained with high probability.