Global biasing using a hardware-based artificial Zeeman term in spinwave Ising machines

Abstract

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.