Advanced For-Loop for QML algorithm search

This paper introduces an advanced framework leveraging Large Language Model-based Multi-Agent Systems (LLMMA) for the automated search and optimization of Quantum Machine Learning (QML) algorithms. Inspired by Google DeepMind's FunSearch, the proposed system works on abstract level to iteratively generates and refines quantum transformations of classical machine learning algorithms (concepts), such as the Multi-Layer Perceptron, forward-forward and backpropagation algorithms. As a proof of concept, this work highlights the potential of agentic frameworks to systematically explore classical machine learning concepts and adapt them for quantum computing, paving the way for efficient and automated development of QML algorithms. Future directions include incorporating planning mechanisms and optimizing strategy in the search space for broader applications in quantum-enhanced machine learning.