  We propose a spintronics-based hardware implementation of neuromorphic
computing, specifically, the spiking neural network, using topological winding
textures in one-dimensional antiferromagnets. The consistency of such a network
is emphasized in light of the conservation of topological charges, and the
natural spatiotemporal interconversions of magnetic winding. We discuss the
realization of the leaky integrate-and-fire behavior of neurons and the
spike-timing-dependent plasticity of synapses. Our proposal opens the
possibility for an all-spin neuromorphic platform based on antiferromagnetic
insulators.
