We present an improved method for quantum machine learning, using a modified Levenberg-Marquardt (LM) method. The LM method is a powerful hybrid gradient-based reinforcement learning technique ideally suited to quantum machine learning, as it only requires knowledge of the final measured output of the quantum computation, not intermediate quantum states, which are generally not accessible without collapsing the quantum state. With this method, we are able to achieve true online training of a quantum system to do a quantum calculation, which, to our knowledge, has never been done before. We demonstrate this using a fundamentally non-classical calculation: estimating the entanglement of an unknown quantum state. Machine learning is applied to learn this algorithm and is demonstrated in simulation and hardware. We show results for two-, three-, four-, five-, six-, seven-, and eight-qubit systems, in Matlab simulations, and, more importantly, these run on the IBM Qiskit hardware interface. With this approach, the quantum system, in a sense, designs its own algorithm. Moreover, the approach enables scaleup, is potentially more efficient, and provides robustness to both noise and decoherence. � 2024 selection and editorial matter, Siddhartha Bhattacharyya, Iv�n Cruz-Aceves, Arpan Deyasi, Pampa Debnath, and Rajarshi Mahapatra; individual chapters, the contributors.