  Collective properties of complex systems composed of many interacting
components such as neurons in our brain can be modeled by artificial networks
based on disordered systems. We show that a disordered neural network of
superconducting loops with Josephson junctions can exhibit computational
properties like categorization and associative memory in the time evolution of
its state in response to information from external excitations. Superconducting
loops can trap multiples of fluxons in many discrete memory configurations
defined by the local free energy minima in the configuration space of all
possible states. A memory state can be updated by exciting the Josephson
junctions to allow the movement of fluxons through the network as the current
through them surpasses their critical current thresholds. Simulations performed
with a lumped element circuit model of a 4-loop network show that information
written through excitations is translated into stable states of trapped flux
and their time evolution. Experimental implementation on a high-Tc
superconductor YBCO-based 4-loop network shows dynamically stable flux flow in
each pathway characterized by the correlations between junction firing
statistics. Neural network behavior is observed as energy barriers separating
state categories in simulations in response to multiple excitations, and
experimentally as junction responses characterizing different flux flow
patterns in the network. The state categories that produce these patterns have
different temporal stabilities relative to each other and the excitations. This
provides strong evidence for time-dependent (short-to-long-term) memories, that
are dependent on the geometrical and junction parameters of the loops, as
described with a network model.
