Machine Learning Experimental Multipartite Entanglement Structure

With the rapid growth of controllable qubits in recent years, experimental multipartite entangled states can be created with high fidelity in various moderate‐ and large‐scale physical systems. However, the characterization of multipartite entanglement structure remains a formidable challenge, as traditionally it requires exponential number of local measurements to realize the identification. Machine learning is demonstrated to be an efficient tool to detect the underlying entanglement structure for ideal states, but it has non‐negligible underperformance when tackling imperfect experimental data in reality. Here, a modified classifier based on feed‐forward neural network to predict experimental entanglement structure in terms of entanglement intactness and depth is proposed. By preprocessing the input data, the classifier maintains efficiency and reliability against experimental noises, with the accuracy being enhanced from 69.7% to 91.2% for 6‐qubit entangled states in spin systems. This method is anticipated to shed light on future studies of entanglement structure, in particular when the number of controlled qubits reaches explosive growth in practice. Machine learning is shown to be an efficient and accurate way to characterize multipartite entanglement structure for noisy experimental states. By training a neural network with just ideal states, entanglement intactness and depth of experimental states can still be predicted accurately, with demonstration on a six‐qubit nuclear magnetic resonance system. This method is ready to be extended to other systems.