Global biasing using a Hardware-based artificial Zeeman term in Spinwave Ising Machines

TL;DR

This paper introduces a hardware-based global biasing method for Spinwave Ising Machines by adding a Zeeman term, enabling the exploration of higher complexity in combinatorial optimization problems.

Contribution

It demonstrates the implementation of a global Zeeman term in a Spinwave Ising Machine, increasing the system's complexity and enabling ferromagnetic ordering despite antiferromagnetic coupling.

Findings

Induced ferromagnetic ordering in spin states

Increased complexity of the Hamiltonian

Enhanced exploration of complex optimization problems

Abstract

A spinwave Ising machine (SWIM) is a newly 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 spin-wave RF pulses in an Yttrium-Iron-Garnet (YIG) film. In this work, we increase the mathematical complexity of the SWIM by adding a global Zeeman term to a 4-spin MAX-CUT Hamiltonian using a continuous external electrical signal with the same frequency as the spin pulses and phase locked with 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 to its Hamiltonian and thus this straightforward implementation helps explore higher degrees of complexity in this evolving solver.