  Conventional digital computation is rapidly approaching physical limits for
speed and energy dissipation. Here we fabricate and test a simple neuromorphic
circuit that models neuronal somas, axons and synapses with superconducting
Josephson junctions. The circuit models two mutually coupled excitatory
neurons. In some regions of parameter space the neurons are desynchronized. In
others, the Josephson neurons synchronize in one of two states, in-phase or
anti-phase. An experimental alteration of the delay and strength of the
connecting synapses can toggle the system back and forth in a phase-flip
bifurcation. Firing synchronization states are calculated >70,000 times faster
than conventional digital approaches. With their speed and low energy
dissipation (10-17 Joules/spike), this set of proof-of- concept experiments
establishes Josephson junction neurons as a viable approach for improvements in
neuronal computation as well as applications in neuromorphic computing.
