Circuits using superconducting single-photon detectors and Josephson junctions to perform signal reception, synaptic weighting, and integration are investigated. The circuits convert photon-detection events into flux quanta, the number of which is determined by the synaptic weight. The current from many synaptic connections is inductively coupled to a superconducting loop that implements the neuronal threshold operation. Designs are presented for synapses and neurons that perform integration as well as detect coincidence events for temporal coding. Both excitatory and inhibitory connections are demonstrated. It is shown that a neuron with a single integration loop can receive input from 1000 such synaptic connections, and neurons of similar design could employ many loops for dendritic processing.