Exploring the Power of Entangled Data in Quantum Machine Learning

Quantum entanglement is a key resource for achieving superiority of quantum computing.Currently, scientists are extensively focusing on how to integrate quantum entanglement into various components of quantum machine learning (QML) models, aiming to surpass the performance of traditional machine learning models.Notable successes include the use of entangled measurements 123 and entangled channels 4 , which have been shown to reduce query complexity or improve the prediction precision for specified QML tasks.Quantum entangled data, capable of encoding more information compared to classical data of the same size, is recognized for its potential to achieve quantum advantages.Nevertheless, the impact of the entanglement degree in quantum data on model performance remains a challenging and unresolved research question.Recently, Wang and collaborators 5 (Nat Commun 2024, 15, 3716) rigorously analyzed the impact of the entanglement degree of quantum data, the number and type of measurements, and the size of training dataset on the prediction error of QML models by establishing the quantum no-free-lunch (NFL) theorem.They consider tasks of quantum dynamics learning with entangled data, which is fundamental to many advanced quantum algorithms, as illustrated in Fig. 1.While conventional understanding suggests that entanglement mainly confers benefits to QML in terms of sample complexity 6,7 , this study demonstrates that the effect of the degree of entanglement on prediction error exhibits a dual effect, that is, whether quantum entanglement improves performance depends on the number of measurements allowed.With a sufficient number of measurements, increasing the entanglement degree in quan-