Transition role of entangled data in quantum machine learning

Xinbiao Wang, Yuxuan Du (), Zhuozhuo Tu, Yong Luo (), Xiao Yuan and Dacheng Tao ()
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Xinbiao Wang: Wuhan University
Yuxuan Du: JD Explore Academy
Zhuozhuo Tu: University of Sydney
Yong Luo: Wuhan University
Xiao Yuan: Peking University
Dacheng Tao: Nanyang Technological University

Nature Communications, 2024, vol. 15, issue 1, 1-8

Abstract: Abstract Entanglement serves as the resource to empower quantum computing. Recent progress has highlighted its positive impact on learning quantum dynamics, wherein the integration of entanglement into quantum operations or measurements of quantum machine learning (QML) models leads to substantial reductions in training data size, surpassing a specified prediction error threshold. However, an analytical understanding of how the entanglement degree in data affects model performance remains elusive. In this study, we address this knowledge gap by establishing a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. Contrary to previous findings, we prove that the impact of entangled data on prediction error exhibits a dual effect, depending on the number of permitted measurements. With a sufficient number of measurements, increasing the entanglement of training data consistently reduces the prediction error or decreases the required size of the training data to achieve the same prediction error. Conversely, when few measurements are allowed, employing highly entangled data could lead to an increased prediction error. The achieved results provide critical guidance for designing advanced QML protocols, especially for those tailored for execution on early-stage quantum computers with limited access to quantum resources.

Date: 2024
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DOI: 10.1038/s41467-024-47983-1

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