  With the goal of understanding the intricate behavior and dynamics of
collections of neurons, we present superconducting circuits containing
Josephson junctions that model biologically realistic neurons. These "Josephson
junction neurons" reproduce many characteristic behaviors of biological neurons
such as action potentials, refractory periods, and firing thresholds. They can
be coupled together in ways that mimic electrical and chemical synapses. Using
existing fabrication technologies, large interconnected networks of Josephson
junction neurons would operate fully in parallel. They would be orders of
magnitude faster than both traditional computer simulations and biological
neural networks. Josephson junction neurons provide a new tool for exploring
long-term large-scale dynamics for networks of neurons.
