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    Probabilistic computing accelerated by spike-frequency adaptation: Applications in integer factorization

    Haijie Xu1,2,*, Cen Wang3,*, Yajun Zhang1,2, Yue Zhang3,†, and Zhe Yuan2,‡

    • *These authors contributed equally to this work.
    • †Contact author: yue-zhang@hust.edu.cn
    • ‡Contact author: yuanz@fudan.edu.cn

    Phys. Rev. Applied 24, 034067 – Published 24 September, 2025

    DOI: https://doi.org/10.1103/dvxz-w9ts

    Abstract

    We develop a local-heating scheme by drawing inspiration from spike-frequency adaptation (SFA) in neuroscience, which naturally fits the present probabilistic computing architecture. The SFA-based approach introduces negative feedback to the individual probabilistic bits (p-bits), effectively lowering the energy gradient in the Ising model and facilitating the system’s escape from local minima in complex energy landscapes. Using integer factorization of semiprime numbers ranging from 16 to 30 bits as a case study, we demonstrate that the SFA algorithm significantly enhances computational efficiency, with an acceleration that exceeds linear scaling with the bit number. We further illustrate the practicality of our SFA algorithm through circuit simulations using stochastic magnetic tunnel junction-based p-bits. This approach not only accelerates integer factorization but also holds promise for addressing other large-scale combinatorial optimization problems, thereby expanding the potential applications of probabilistic computing.

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