A spin Hall Ising machine.

ORAL  · Invited

Abstract

Ising Machines (IMs) are physical systems designed to find solutions to combinatorial optimization (CO) problems mapped onto the IM via the coupling strengths of its binary spins. Using the intrinsic dynamics and different annealing schemes, the IM relaxes over time to its lowest energy state, which is the solution to the CO problem. Here we present the world's most miniaturized, and the first spin Hall nano-oscillator (SHNO) based Ising machine. One of the most intriguing properties of SHNOs is their ability to synchronize to each other and to an external source. We demonstrate robust phase binarization due to injection locking at twice the natural frequency of SHNOs and analyze the binarization behavior as a function of injection locking power and frequency.  We then show binarization in 1x2 and 2x2 SHNO interconnected arrays. The phase binarization manifests itself as distinct microwave output power levels, which are readily distinguished using electrical means. In addition, we use phase-resolved Brillouin Light Scattering (phase-BLS) microscopy to directly observe the individual phases of the precessing magnetization in each nano-constriction. The different states can be accessed using either different injected power levels or a detuned frequency of the injected signal. We then propose pathways to control the coupling between SHNOs in order to gain flexibility in terms of mapped problems, and realize truly miniaturized, ultra-fast, and large-scale oscillator-based Ising Machines.

*This work was partially supported by the Horizon 2020 research and innovation program (ERC Advanced Grant No.~835068 "TOPSPIN"). This work was also partially supported by the Swedish Research Council (VR) and the Knut and Alice Wallenberg Foundation. J.Ch. acknowledges funding from program No. 2017/24/T/ST3/00009 by National Science Center, Poland. We acknowledge D-Wave Systems Inc. for providing access to quantum computing technology via their cloud service LeapTM.

–

Publication: "Phase-binarized spin Hall nano-oscillator arrays: Towards spin Hall Ising machines"; Under consideration at PRA.

Presenters

  • Afshin Houshang

    • University of Gothenburg
    • 1Physics Department, University of Gothenburg, 41296 Gothenburg, Sweden.
    • Physics Department, University of Gothenburg

Authors

  • Afshin Houshang

    • University of Gothenburg
    • 1Physics Department, University of Gothenburg, 41296 Gothenburg, Sweden.
    • Physics Department, University of Gothenburg

  • Mohammad Zahedinejad

    • Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden

  • Shreyas Muralidhar

    • Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden

  • Roman Khymyn

    • University of Gothenburg, Sweden
    • University of Gothenburg
    • Physics Department, University of Gothenburg
    • Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden

  • Mona Rajabali

    • University of Gothenburg

  • Himanshu Fulara

    • Indian Institute of Technology Roorkee
    • 1Physics Department, University of Gothenburg, 41296 Gothenburg, Sweden. 2Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667, India
    • Indian Institute of Technology Roorkee, India
    • Physics Department, University of Gothenburg

  • Ahmad Awad

    • Gothenburg University
    • Physics Department, University of Gothenburg

  • Johan Åkerman

    • Goteborg Univ
    • University of Gothenburg
    • 1Physics Department, University of Gothenburg, 41296 Gothenburg, Sweden.
    • University of Gothenburg, Sweden
    • Physics Department, University of Gothenburg
    • Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden

  • Jakub Checinski

    • AGH University of Science and Technology, Institute of Electronics, Al. Mickiewicza 30, 30-059 Krakow, Poland

  • Mykola Dvornik

    • NanOsc AB
    • NanOsc AB, Gothenburg, Sweden.
    • University of Gothenburg, Sweden
    • Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden.