  Neural networks have proven effective for solving many difficult
computational problems. Implementing complex neural networks in software is
very computationally expensive. To explore the limits of information
processing, it will be necessary to implement new hardware platforms with large
numbers of neurons, each with a large number of connections to other neurons.
Here we propose a hybrid semiconductor-superconductor hardware platform for the
implementation of neural networks and large-scale neuromorphic computing. The
platform combines semiconducting few-photon light-emitting diodes with
superconducting-nanowire single-photon detectors to behave as spiking neurons.
These processing units are connected via a network of optical waveguides, and
variable weights of connection can be implemented using several approaches. The
use of light as a signaling mechanism overcomes fanout and parasitic
constraints on electrical signals while simultaneously introducing physical
degrees of freedom which can be employed for computation. The use of
supercurrents achieves the low power density necessary to scale to systems with
enormous entropy. The proposed processing units can operate at speeds of at
least $20$ MHz with fully asynchronous activity, light-speed-limited latency,
and power densities on the order of 1 mW/cm$^2$ for neurons with 700
connections operating at full speed at 2 K. The processing units achieve an
energy efficiency of $\approx 20$ aJ per synapse event. By leveraging
multilayer photonics with deposited waveguides and superconductors with feature
sizes $>$ 100 nm, this approach could scale to systems with massive
interconnectivity and complexity for advanced computing as well as explorations
of information processing capacity in systems with an enormous number of
information-bearing microstates.
