Quantum learning advantage on a scalable photonic platform

Recent advances in quantum technologies have demonstrated that quantum systems can outperform classical ones in specific tasks, a concept known as quantum advantage. Although previous efforts have focused on computational speedups, a definitive and provable quantum advantage that is unattainable by any classical system has remained elusive. In this work, we demonstrate a provable photonic quantum advantage by implementing a quantum-enhanced protocol for learning a high-dimensional physical process. Using imperfect Einstein–Podolsky–Rosen entanglement, we achieve a sample complexity reduction of 11.8 orders of magnitude compared to classical methods without entanglement. These results show that large-scale, provable quantum advantage is achievable with current photonic technology and represent a key step toward practical quantum-enhanced learning protocols in quantum metrology and machine learning.

Z.-H.L., R.B., E.E.B.Ø., O.C., J.A.H.N., J.S.N.-N., and U.L.A. acknowledge support from the Danish National Research Foundation, Center for Macroscopic Quantum States (bigQ, DNRF0142), EU project CLUSTEC (grant agreement no. 101080173), EU ERC project ClusterQ (grant agreement no. 101055224), NNF project CBQS (NNF 24SA0088433), Innovation Fund Denmark (PhotoQ project, grant no. 1063-00046A), and the MSCA European Postdoctoral Fellowships (GTGBS, project no. 101106833). J.P. acknowledges support from the US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (DE-NA0003525, DE-SC0020290), the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the National Science Foundation (PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center. L.J. acknowledges support from the ARO(W911NF-23-1-0077), ARO MURI (W911NF-21-1-0325), AFOSR MURI (FA9550-19-1-0399, FA9550-21-1-0209, FA9550-23-1-0338), DARPA (HR0011-24-9-0359, HR0011-24-9-0361), NSF (OMA-1936118, ERC-1941583, OMA-2137642, OSI-2326767, CCF-2312755), NTT Research, and the Packard Foundation (2020-71479). S.Z. acknowledges funding provided by Perimeter Institute for Theoretical Physics, a research institute supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. C.O. was supported by the National Research Foundation of Korea grants (nos. RS-2024-00431768 and RS-2025-00515456) funded by the Korean government [Ministry of Science and ICT (MSIT)] and the Institute of Information & Communications Technology Planning & Evaluation (IITP) grants funded by the Korea government (MSIT) (nos. IITP-2025-RS-2025-02283189 and IITP-2025-RS-2025-02263264).

Supplementary Materials (PDF):

Supplementary Text; Figs. S1 to S10; Tables S1 to S3; References (34–40); Algorithms S1 and S2.