IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v13y2022i1d10.1038_s41467-022-34847-9.html
   My bibliography  Save this article

Multidimensional hyperspin machine

Author

Listed:
  • Marcello Calvanese Strinati

    (Centro Ricerche Enrico Fermi (CREF)
    Institute for Complex Systems, National Research Council (ISC-CNR))

  • Claudio Conti

    (Centro Ricerche Enrico Fermi (CREF)
    Institute for Complex Systems, National Research Council (ISC-CNR)
    Sapienza University of Rome)

Abstract

From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin models, but only for Ising or low-dimensional spins. Currently, machines implementing arbitrary dimensions remain a challenge. Here, we introduce and validate a hyperspin machine to simulate multidimensional continuous spin models. We realize high-dimensional spins by pumping groups of parametric oscillators, and show that the hyperspin machine finds to a very good approximation the ground state of complex graphs. The hyperspin machine can interpolate between different dimensions by tuning the coupling topology, a strategy that we call “dimensional annealing”. When interpolating between the XY and the Ising model, the dimensional annealing substantially increases the success probability compared to conventional Ising simulators. Hyperspin machines are a new computational model for combinatorial optimization. They can be realized by off-the-shelf hardware for ultrafast, large-scale applications in classical and quantum computing, condensed-matter physics, and fundamental studies.

Suggested Citation

  • Marcello Calvanese Strinati & Claudio Conti, 2022. "Multidimensional hyperspin machine," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-34847-9
    DOI: 10.1038/s41467-022-34847-9
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/s41467-022-34847-9
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1038/s41467-022-34847-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Gilli, Manfred & Maringer, Dietmar & Schumann, Enrico, 2011. "Numerical Methods and Optimization in Finance," Elsevier Monographs, Elsevier, edition 1, number 9780123756626.
    2. Fabian Böhm & Guy Verschaffelt & Guy Van der Sande, 2019. "A poor man’s coherent Ising machine based on opto-electronic feedback systems for solving optimization problems," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    3. Yoshitomo Okawachi & Mengjie Yu & Jae K. Jang & Xingchen Ji & Yun Zhao & Bok Young Kim & Michal Lipson & Alexander L. Gaeta, 2020. "Demonstration of chip-based coupled degenerate optical parametric oscillators for realizing a nanophotonic spin-glass," Nature Communications, Nature, vol. 11(1), pages 1-7, December.
    4. M. W. Johnson & M. H. S. Amin & S. Gildert & T. Lanting & F. Hamze & N. Dickson & R. Harris & A. J. Berkley & J. Johansson & P. Bunyk & E. M. Chapple & C. Enderud & J. P. Hilton & K. Karimi & E. Ladiz, 2011. "Quantum annealing with manufactured spins," Nature, Nature, vol. 473(7346), pages 194-198, May.
    5. Joseph W. Britton & Brian C. Sawyer & Adam C. Keith & C.-C. Joseph Wang & James K. Freericks & Hermann Uys & Michael J. Biercuk & John J. Bollinger, 2012. "Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins," Nature, Nature, vol. 484(7395), pages 489-492, April.
    6. David I. Graham & Matthew J. Craven, 2021. "An exact algorithm for small-cardinality constrained portfolio optimisation," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(6), pages 1415-1431, June.
    7. Nicolas Rougemaille & Benjamin Canals, 2019. "Cooperative magnetic phenomena in artificial spin systems: spin liquids, Coulomb phase and fragmentation of magnetism – a colloquium," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(3), pages 1-30, March.
    8. Takahiro Inagaki & Kensuke Inaba & Timothée Leleu & Toshimori Honjo & Takuya Ikuta & Koji Enbutsu & Takeshi Umeki & Ryoichi Kasahara & Kazuyuki Aihara & Hiroki Takesue, 2021. "Collective and synchronous dynamics of photonic spiking neurons," Nature Communications, Nature, vol. 12(1), pages 1-8, December.
    9. K. Kim & M.-S. Chang & S. Korenblit & R. Islam & E. E. Edwards & J. K. Freericks & G.-D. Lin & L.-M. Duan & C. Monroe, 2010. "Quantum simulation of frustrated Ising spins with trapped ions," Nature, Nature, vol. 465(7298), pages 590-593, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tinish Bhattacharya & George H. Hutchinson & Giacomo Pedretti & Xia Sheng & Jim Ignowski & Thomas Vaerenbergh & Ray Beausoleil & John Paul Strachan & Dmitri B. Strukov, 2024. "Computing high-degree polynomial gradients in memory," Nature Communications, Nature, vol. 15(1), pages 1-11, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juntao Wang & Daniel Ebler & K. Y. Michael Wong & David Shui Wing Hui & Jie Sun, 2023. "Bifurcation behaviors shape how continuous physical dynamics solves discrete Ising optimization," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    2. Fabian Böhm & Diego Alonso-Urquijo & Guy Verschaffelt & Guy Van der Sande, 2022. "Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    3. Marc S. Paolella, 2014. "Fast Methods For Large-Scale Non-Elliptical Portfolio Optimization," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 1-32.
    4. Kapetanios, George & Marcellino, Massimiliano & Papailias, Fotis, 2016. "Forecasting inflation and GDP growth using heuristic optimisation of information criteria and variable reduction methods," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 369-382.
    5. Byron Tasseff & Tameem Albash & Zachary Morrell & Marc Vuffray & Andrey Y. Lokhov & Sidhant Misra & Carleton Coffrin, 2024. "On the emerging potential of quantum annealing hardware for combinatorial optimization," Journal of Heuristics, Springer, vol. 30(5), pages 325-358, December.
    6. Cahuc, Pierre & Malherbet, Franck & Prat, Julien, 2019. "The Detrimental Effect of Job Protection on Employment: Evidence from France," IZA Discussion Papers 12384, Institute of Labor Economics (IZA).
    7. Ferenc Iglói & Cécile Monthus, 2018. "Strong disorder RG approach – a short review of recent developments," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(11), pages 1-25, November.
    8. Manfred Gilli & Enrico Schumann, 2012. "Heuristic optimisation in financial modelling," Annals of Operations Research, Springer, vol. 193(1), pages 129-158, March.
    9. Xunzhao Yin & Yu Qian & Alptekin Vardar & Marcel Günther & Franz Müller & Nellie Laleni & Zijian Zhao & Zhouhang Jiang & Zhiguo Shi & Yiyu Shi & Xiao Gong & Cheng Zhuo & Thomas Kämpfe & Kai Ni, 2024. "Ferroelectric compute-in-memory annealer for combinatorial optimization problems," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    10. Xiaoyu Zhang & Ayhan Duzgun & Yuyang Lao & Shayaan Subzwari & Nicholas S. Bingham & Joseph Sklenar & Hilal Saglam & Justin Ramberger & Joseph T. Batley & Justin D. Watts & Daniel Bromley & Rajesh V. C, 2021. "String Phase in an Artificial Spin Ice," Nature Communications, Nature, vol. 12(1), pages 1-7, December.
    11. Manuel Kleinknecht & Wing Lon Ng, 2015. "Minimizing Basel III Capital Requirements with Unconditional Coverage Constraint," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 22(4), pages 263-281, October.
    12. Longbing Cao, 2021. "AI in Finance: Challenges, Techniques and Opportunities," Papers 2107.09051, arXiv.org.
    13. Andreas Wichert, 2022. "Quantum Tree Search with Qiskit," Mathematics, MDPI, vol. 10(17), pages 1-28, August.
    14. De Haas Samuel & Winker Peter, 2016. "Detecting Fraudulent Interviewers by Improved Clustering Methods – The Case of Falsifications of Answers to Parts of a Questionnaire," Journal of Official Statistics, Sciendo, vol. 32(3), pages 643-660, September.
    15. Capuozzo, Pietro & Panella, Emanuele & Schettini Gherardini, Tancredi & Vvedensky, Dimitri D., 2021. "Path integral Monte Carlo method for option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    16. Singh, Vikas Vikram & Lisser, Abdel & Arora, Monika, 2021. "An equivalent mathematical program for games with random constraints," Statistics & Probability Letters, Elsevier, vol. 174(C).
    17. Samuel Fern'andez-Lorenzo & Diego Porras & Juan Jos'e Garc'ia-Ripoll, 2020. "Hybrid quantum-classical optimization for financial index tracking," Papers 2008.12050, arXiv.org, revised Oct 2021.
    18. 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.
    19. Stefan Andreea-Mirabela, 2020. "Metaheuristichybridization: Memeticalgorithm," Annals of University of Craiova - Economic Sciences Series, University of Craiova, Faculty of Economics and Business Administration, vol. 1(48), pages 155-164, August.
    20. Miśkiewicz, Janusz, 2013. "Power law classification scheme of time series correlations. On the example of G20 group," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2150-2162.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-34847-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.nature.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.