We fabricated neural-based superconducting integrated-circuits by usin
g Nb/AlOx/Nb Josephson junctions, and demonstrated circuit operation o
f 2-bit neural-based A/D converter as an example of optimization probl
em. We used, in the present superconducting neural circuits, fluxon pu
lses as the neural impulses and a Josephson junction as a threshold el
ement to achieve an advanced operation. The integrative time delays du
e to the inductance of superconducting circuits correspond to those du
e to capacitance in real neurons. The values of resistor by which Jose
phson transmission lines are connected represent fixed synaptic streng
thes. The preliminary experimental result suggests that variable criti
cal currents of d.c.SQUID may provide synapses with variable strength.
In our implementation scheme, complex circuit design can easily be re
alized by connecting Josephson transmission lines. In order to design
complex circuits like a Hopfield neural network, we propose a new meth
od which can be used to analyze the properties of local minima in the
energy function. A novel design technique to eliminate these local min
ima in the networks has been developed. It is useful for hardware stud
ies on artificial neural networks using superconductor and semiconduct
or.