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Integer factorization using stochastic magnetic tunnel junctions

Author

Listed:
  • William A. Borders

    (Tohoku University)

  • Ahmed Z. Pervaiz

    (Purdue University)

  • Shunsuke Fukami

    (Tohoku University
    Tohoku University
    Tohoku University
    Tohoku University)

  • Kerem Y. Camsari

    (Purdue University)

  • Hideo Ohno

    (Tohoku University
    Tohoku University
    Tohoku University
    Tohoku University)

  • Supriyo Datta

    (Purdue University)

Abstract

Conventional computers operate deterministically using strings of zeros and ones called bits to represent information in binary code. Despite the evolution of conventional computers into sophisticated machines, there are many classes of problems that they cannot efficiently address, including inference, invertible logic, sampling and optimization, leading to considerable interest in alternative computing schemes. Quantum computing, which uses qubits to represent a superposition of 0 and 1, is expected to perform these tasks efficiently1–3. However, decoherence and the current requirement for cryogenic operation4, as well as the limited many-body interactions that can be implemented, pose considerable challenges. Probabilistic computing1,5–7 is another unconventional computation scheme that shares similar concepts with quantum computing but is not limited by the above challenges. The key role is played by a probabilistic bit (a p-bit)—a robust, classical entity fluctuating in time between 0 and 1, which interacts with other p-bits in the same system using principles inspired by neural networks8. Here we present a proof-of-concept experiment for probabilistic computing using spintronics technology, and demonstrate integer factorization, an illustrative example of the optimization class of problems addressed by adiabatic9 and gated2 quantum computing. Nanoscale magnetic tunnel junctions showing stochastic behaviour are developed by modifying market-ready magnetoresistive random-access memory technology10,11 and are used to implement three-terminal p-bits that operate at room temperature. The p-bits are electrically connected to form a functional asynchronous network, to which a modified adiabatic quantum computing algorithm that implements three- and four-body interactions is applied. Factorization of integers up to 945 is demonstrated with this rudimentary asynchronous probabilistic computer using eight correlated p-bits, and the results show good agreement with theoretical predictions, thus providing a potentially scalable hardware approach to the difficult problems of optimization and sampling.

Suggested Citation

  • William A. Borders & Ahmed Z. Pervaiz & Shunsuke Fukami & Kerem Y. Camsari & Hideo Ohno & Supriyo Datta, 2019. "Integer factorization using stochastic magnetic tunnel junctions," Nature, Nature, vol. 573(7774), pages 390-393, September.
  • Handle: RePEc:nat:nature:v:573:y:2019:i:7774:d:10.1038_s41586-019-1557-9
    DOI: 10.1038/s41586-019-1557-9
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    Citations

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    Cited by:

    1. Nihal Sanjay Singh & Keito Kobayashi & Qixuan Cao & Kemal Selcuk & Tianrui Hu & Shaila Niazi & Navid Anjum Aadit & Shun Kanai & Hideo Ohno & Shunsuke Fukami & Kerem Y. Camsari, 2024. "CMOS plus stochastic nanomagnets enabling heterogeneous computers for probabilistic inference and learning," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    2. Hakseung Rhee & Gwangmin Kim & Hanchan Song & Woojoon Park & Do Hoon Kim & Jae Hyun In & Younghyun Lee & Kyung Min Kim, 2023. "Probabilistic computing with NbOx metal-insulator transition-based self-oscillatory pbit," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    3. Kyung Seok Woo & Jaehyun Kim & Janguk Han & Woohyun Kim & Yoon Ho Jang & Cheol Seong Hwang, 2022. "Probabilistic computing using Cu0.1Te0.9/HfO2/Pt diffusive memristors," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    4. M. A. Weiss & A. Herbst & J. Schlegel & T. Dannegger & M. Evers & A. Donges & M. Nakajima & A. Leitenstorfer & S. T. B. Goennenwein & U. Nowak & T. Kurihara, 2023. "Discovery of ultrafast spontaneous spin switching in an antiferromagnet by femtosecond noise correlation spectroscopy," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    5. Xing Chen & Flavio Abreu Araujo & Mathieu Riou & Jacob Torrejon & Dafiné Ravelosona & Wang Kang & Weisheng Zhao & Julie Grollier & Damien Querlioz, 2022. "Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    6. Chao Yun & Zhongyu Liang & Aleš Hrabec & Zhentao Liu & Mantao Huang & Leran Wang & Yifei Xiao & Yikun Fang & Wei Li & Wenyun Yang & Yanglong Hou & Jinbo Yang & Laura J. Heyderman & Pietro Gambardella , 2023. "Electrically programmable magnetic coupling in an Ising network exploiting solid-state ionic gating," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    7. ZhuangEn Fu & Piumi I. Samarawickrama & John Ackerman & Yanglin Zhu & Zhiqiang Mao & Kenji Watanabe & Takashi Taniguchi & Wenyong Wang & Yuri Dahnovsky & Mingzhong Wu & TeYu Chien & Jinke Tang & Allan, 2024. "Tunneling current-controlled spin states in few-layer van der Waals magnets," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    8. John Daniel & Zheng Sun & Xuejian Zhang & Yuanqiu Tan & Neil Dilley & Zhihong Chen & Joerg Appenzeller, 2024. "Experimental demonstration of an on-chip p-bit core based on stochastic magnetic tunnel junctions and 2D MoS2 transistors," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    9. Srijan Nikhar & Sidharth Kannan & Navid Anjum Aadit & Shuvro Chowdhury & Kerem Y. Camsari, 2024. "All-to-all reconfigurability with sparse and higher-order Ising machines," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    10. Jérémie Laydevant & Danijela Marković & Julie Grollier, 2024. "Training an Ising machine with equilibrium propagation," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    11. Takuya Funatsu & Shun Kanai & Jun’ichi Ieda & Shunsuke Fukami & Hideo Ohno, 2022. "Local bifurcation with spin-transfer torque in superparamagnetic tunnel junctions," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    12. Jia Si & Shuhan Yang & Yunuo Cen & Jiaer Chen & Yingna Huang & Zhaoyang Yao & Dong-Jun Kim & Kaiming Cai & Jerald Yoo & Xuanyao Fong & Hyunsoo Yang, 2024. "Energy-efficient superparamagnetic Ising machine and its application to traveling salesman problems," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    13. Kang Wang & Yiou Zhang & Vineetha Bheemarasetty & Shiyu Zhou & See-Chen Ying & Gang Xiao, 2022. "Single skyrmion true random number generator using local dynamics and interaction between skyrmions," Nature Communications, Nature, vol. 13(1), pages 1-8, December.

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