  Atomic synapses represent a special class of memristors whose operation
relies on the formation of metallic nanofilaments bridging two electrodes
across an insulator. Due to the magnifying effect of this narrowest
cross-section on the device conductance, a nanometer scale displacement of a
few atoms grants access to various resistive states at ultimately low energy
costs, satisfying the fundamental requirements of neuromorphic computing
hardware. Yet, device engineering lacks the complete quantum characterization
of such filamentary conductance. Here we analyze multiple Andreev reflection
processes emerging at the filament terminals when superconducting electrodes
are utilized. Thereby the quantum PIN code, i.e. the transmission probabilities
of each individual conduction channel contributing to the conductance of the
nanojunctions is revealed. Our measurements on Nb$_2$O$_5$ resistive switching
junctions provide a profound experimental evidence that the onset of the high
conductance ON state is manifested via the formation of truly atomic-sized
metallic filaments.
