  Neuromorphic computing which aims to mimic the collective and emergent
behavior of the brain's neurons, synapses, axons, dendrites offers an
intriguing, potentially disruptive solution to society's ever-growing
computational needs. Although much progress has been made in designing circuit
elements that mimic the behavior of neurons and synapses, challenges remain in
designing networks of elements that feature a collective response behavior. We
present simulations of networks of circuits and devices based on
superconducting and Mott-insulating oxides that display a multiplicity of
emergent states that depend on the spatial configuration of the network. Our
proposed network designs are based on experimentally known ways of tuning the
properties of these oxides using light ions. We show how neuronal and synaptic
behavior can be achieved with arrays of superconducting Josephson junction
loops, all within the same device. We also show how a multiplicity of synaptic
states could be achieved by designing arrays of devices based on hydrogenated
rare-earth nickelates. Together, our results demonstrate a new research
platform that utilizes the collective macroscopic properties of quantum
materials to mimic the emergent behavior found in biological systems.
