This study investigates the impact of entanglement in training data on the performance of quantum machine learning (QML) models for learning quantum dynamics. Contrary to previous assumptions, the authors prove a quantum no-free-lunch (NFL) theorem demonstrating a dual effect of entangled data on prediction error, dependent on the number of permitted measurements. With sufficient measurements, increasing entanglement consistently reduces prediction error or decreases the required training data size. Conversely, with few measurements, highly entangled data can increase prediction error. The findings provide crucial guidance for designing QML protocols, especially for resource-constrained early-stage quantum computers.

Xinbiao Wang, Yuxuan Du, Zhuozhuo Tu, Yong Luo, Xiao Yuan, Dacheng Tao