Ultrafast Ising Machines using spin torque nano-oscillators

Abstract

Combinatorial optimization problems are known for being particularly hard to solve on traditional von Neumann architectures. This has led to the development of Ising Machines (IMs) based on quantum annealers and optical and electronic oscillators, demonstrating speed-ups compared to central processing unit (CPU) and graphics processing unit (GPU) algorithms. Spin torque nano-oscillators (STNOs) have shown GHz operating frequency, nanoscale size, and nanosecond turn-on time, which would allow their use in ultrafast oscillator-based IMs. Here, we show using numerical simulations based on STNO auto-oscillator theory that STNOs exhibit fundamental characteristics needed to realize IMs, including in-phase/out-of-phase synchronization and second harmonic injection locking phase binarization. Furthermore, we demonstrate numerically that large STNO network IMs can solve Max-Cut problems on nanosecond timescales.

Advances in Magnetics Roadmap on Spin-Wave Computing

“…Two-dimensional arrays of SHNOs can also be phasebinarized and then used as oscillator based Ising Machines [416], [417], where they can lead to orders of magnitude smaller, faster, and less power-hungry solvers of combinatorial optimization problems compared to existing commercial solutions.…”

Fabrication of voltage-gated spin Hall nano-oscillators

“…This has resulted in a new class of nanoscopic wideband microwave oscillators known as spin Hall nano-oscillators (SHNOs) [13][14][15][16][17][18][19][20][21][22][23][24][25] , which may be viewed as successors to the earlier spin torque nano-oscillators 17,26 . SHNOs have been studied in a wide range of geometries such as nano-pillars 12 , nano-gaps 13,16 , nano-wires 14,27,28 and nano-constrictions 15,19 , where the nanoconstrictions stand out as particularly promising and versatile thanks to their ease of fabrication, direct optical access to the magnetodynamical region 15,23,29,30 , a propensity for mutual synchronization in linear chains 31 and two-dimensional arrays 32 , affording them an order of magnitude higher quality factors, and easy implementation of neuromorphic computing concepts [32][33][34][35][36][37] .…”

Creating electronic oscillator-based Ising machines without external injection locking

“…The Ising model, originally developed for spin glass systems 1 , has recently experienced renewed attention owing to its application in accelerating computationally hard problems which are still considered intractable to solve using conventional digital computers. This is motivated by the fact that a large number of such problems 2 – 6 can be directly mapped to the Ising Hamiltonian: , where is the i th spin ( ), is interaction coefficient between spin i and spin j , and N is the total number of spins in the system; the self-interaction term ( ) in the Ising Hamiltonian has been neglected here. For instance, consider the combinatorial optimization-based Maximum Cut (MaxCut) problem—the benchmark problem considered in this work—which entails computing a cut that divides the nodes of the graph in two sets (S1, S2) such that the number of common edges among the two sets is as large as possible.…”