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    Co-designed counterdiabatic quantum optimization on a photonic quantum processor

    Xiao-Wen Shang1,2,3,*, Xuan Chen1,2,*, Narendra N. Hegade4, Ze-Feng Lan1,2, Hao Tang1,2,†, Jian-Peng Dou1,2, Xuan-Kun Li1,2, Yu-Quan Peng3, Enrique Solano4 et al.

    Xian-Min Jin1,2,3,5,‡

    • 1Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Photonics and Communications, Shanghai Jiao Tong University, Shanghai 200240, China
    • 2Hefei National Laboratory, Hefei 230088, China
    • 3TuringQ Co., Ltd., Shanghai 200240, China
    • 4Kipu Quantum GmbH, Greifswalderstrasse 212, 10405 Berlin, Germany
    • 5Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China

    • *These authors contributed equally to this work.
    • †Contact author: htang2015@sjtu.edu.cn
    • ‡Contact author: xianmin.jin@sjtu.edu.cn

    Phys. Rev. Applied 25, 064026 – Published 5 June, 2026

    DOI: https://doi.org/10.1103/7gl4-zrh6

    Abstract

    Hardware-algorithm co-design provides an effective route for implementing quantum optimization on near-term hardware. Counterdiabatic (CD) protocols can accelerate adiabatic optimization but are difficult to realize digitally due to increased circuit depth and noise sensitivity. Here, we report a photonic co-design strategy that directly implements CD dynamics on a programmable photonic integrated circuit based on a Mach-Zehnder interferometer mesh. By exploiting the ability of the photonic processor to realize arbitrary unitary transformations, our approach bypasses gate-level decomposition and significantly reduces circuit depth. We further enhance the protocol by mitigating higher-order many-body terms in conventional CD optimization. An experimental demonstration of integer factorization achieves success probabilities up to 86% with only three layers, together with accelerated energy convergence, highlighting programmable photonic platforms for quantum optimization.

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