Victor H. González

Optical coherent Ising machines based on time-multiplexing have demonstrated significant progress in terms of connectivity and spin scalability. However, they are constrained by large physical footprints, high power consumption, poor thermal stability, and high cost. Here, we present a time-multiplexed Ising machine leveraging propagating wave packets in solid-state delay lines at radio frequencies, enabling thermally stable, robust, low-power, tabletop, and affordable design. We use two serially connected 20.5 MHz, 707 μ s bulk acoustic wave delay lines supporting 2048 spins. Our design provides all-to-all connectivity with 15-bit coupling resolution and finds approximate MAX-CUT solutions in 341 ms, potentially scalable to sub-ms by using higher frequency delay lines. Additionally, we demonstrate solutions to number partitioning and Sudoku problems. Compared with state-of-the-art Coherent Ising machines, our machine exhibits four orders of magnitude higher thermal stability. Against the simulated bifurcation algorithm, our design achieves comparable results on the MAX-CUT problem, while outperforming it on the more complex number-partitioning and Sudoku problems.

Spin–orbit torque can drive auto-oscillations of propagating spin-wave modes in nano-constriction spin Hall nano-oscillators. These modes facilitate both long-range coupling and the possibility of controlling their phase, which is a crucial aspect for device application. Here, we demonstrate variable-phase coupling between two nano-constriction spin Hall nano-oscillators and their mutual synchronization driven by propagating spin waves. Using electrical measurements and phase-resolved micro-focused Brillouin light scattering microscopy, we show that the phase of the mutual synchronization can be tuned by modulating the drive current or the applied field. Our micromagnetic simulations explore the phase tunability using voltage gating. Our results advance the capabilities of mutually synchronized spin Hall nano-oscillators and open the possibilities for applications in spin-wave logic-based devices.

A spinwave Ising machine (SWIM) is a recently proposed type of time-multiplexed hardware solver for combinatorial optimization that employs feedback coupling and phase sensitive amplification to map an Ising Hamiltonian into phase-binarized propagating spinwave RF pulses in an Yttrium-Iron-Garnet film. In this work, we increase the mathematical complexity of the SWIM by adding a global Zeeman term to a 4-spin nearest neighbor Hamiltonian using a continuous external electrical signal with the same frequency as the spin pulses and phase locked with one of the two possible states. We are able to induce ferromagnetic ordering in both directions of the spin states despite antiferromagnetic pairwise coupling. Embedding a planar antiferromagnetic spin system in a magnetic field has been proven to increase the complexity of the graph associated with its Hamiltonian, and, thus, this straightforward implementation helps explore higher degrees of complexity in this evolving solver.

Time-multiplexed Coherent Ising Machines (CIMs) have demonstrated promising results in rapidly solving large-scale combinatorial problems. However, CIMs remain relatively large and power-demanding. Here, we demonstrate a spinwave-based Ising machine (SWIM) that due to the low spinwave group velocity allows for sufficient miniaturization and reduced power consumption. The SWIM is implemented using a 10-mm-long 5-μm-thick Yttrium Iron Garnet film with off-the-shelf microwave components and can support an 8-spin MAX-CUT problem and solve it in less than 4 μs consuming only 7 μJ. As the SWIM minimizes its energy, we observe that the spin states can demonstrate both uniform and domain-propagation-like switching. The developed SWIM has the potential for substantial further miniaturization with reduction of power consumption, scalability in the number of supported spins, increase of operational speed, and may become a versatile platform for commercially feasible high-performance solvers of combinatorial optimization problems.