◄ UD0   spin   transmon (the qubit)   the J-junction <•
Perceptron theory · the substrate jump · the seventh body

The perceptron in a Josephson junction

The fastest body, and the last classical one before the world goes quantum. Two superconductors joined at a weak link carry a current with no voltage and no loss — until you push past a critical current, and the junction snaps to life, spitting out information one flux quantum at a time, in picoseconds, for attojoules. The threshold isn't bolted on; it's a phase particle escaping a tilted washboard. And the very same junction, given a capacitor, becomes the qubit — so this is the door from the neuron to the quantum.
weight/input = bias currents  ·  threshold = critical current Ic (the washboard escape)  ·  spike = one flux quantum Φ₀ = h/2e  ·  speed = picoseconds, ~aJ
✓ STRONG

The junction & the SFQ pulse. Josephson 1962 (Nobel); RSFQ logic (Likharev); SQUIDs in every MRI. The threshold and the single-flux-quantum spike are bedrock — the fastest, lowest-energy switch known.

◐ MIDDLING

Superconducting neuromorphic. JJ integrate-and-fire neurons and SFQ neural nets are demonstrated — genuinely fast and efficient, but they live at 4 K. The cryostat is the cost.

◔ FRONTIER

The quantum neuron. A junction + capacitor is a transmon qubit; the phase becomes quantum. Quantum perceptrons / large superconducting nets are open — the door this body opens.

I · The threshold is a particle escaping a washboard

A biased junction behaves like a marble on a tilted washboard — the potential U(φ) = −E_J cos φ − (ℏ/2e)·I·φ. The two Josephson relations run the show: I = Ic·sin φ   ·   dφ/dt = 2eV/ℏ Below the critical current the marble is trapped in a well — the phase is pinned, there's zero voltage, a perfect dissipationless supercurrent. Tilt past Ic and the wells vanish: the marble runs downhill, and every well it rolls over slips one flux quantum through the junction — a voltage spike. That escape is the neuron's threshold.

the tilted washboard U(φ) · the phase marble · trapped (V=0, supercurrent) below Ic · running & emitting flux quanta above Ic
SUPERCURRENT · V=0
junction regime
0
flux quanta emitted (Φ₀ each)
multiply/sum= bias currents add (Kirchhoff)threshold= the critical current Icspike= a 2π phase slip = one Φ₀
Below Ic, nothing moves and nothing dissipates — that's the magic of superconductivity put to work as a resting neuron. The instant you cross Ic the silence breaks into a stream of identical, quantized pulses.

II · The single-flux-quantum spiking neuron

Wire the weighted inputs in as bias current and the junction is an integrate-and-fire neuron with no extra parts: sub-threshold input leaks away as supercurrent; cross Ic and it fires a quantized SFQ pulse, the phase slips by 2π, and it resets — automatically. Every spike is identical and carries exactly one flux quantum. And it does this in picoseconds, dissipating attojoules — the fastest, leanest neuron physics offers.

accumulated phase (sawtooth) resets by 2π at each fire · the SFQ pulse train below · firing rate ∝ how far input exceeds Ic
SILENT
below Ic = no spikes
0
SFQ pulses (this window)

Quantized, self-resetting, identical spikes — a junction is almost suspiciously well-suited to be a neuron. The catch is the same as all of superconducting computing: it only works cold, and getting signals in and out of the cryostat is its own art.

III · It learns, it opens onto the qubit, and it fits in folders

Same rule, same result — AND/OR in a few sweeps, XOR stuck at 3/4 (verified), freed by a second junction layer. But this body has two endings the others don't. First: add a capacitor and the washboard becomes a quantum well — the phase is now an operator, the lowest two levels are a transmon qubit, and the classical neuron becomes a quantum one. Second: a junction is just two superconductors joined at a weak link — which is literally the ROOT0 <• — so you can build a working one out of folders.

target:
press train
the junction, as folders  <•
the-virtual-junction/ electrode-left/ < the < arm (a superconductor) the-dot/ • the weak link — φ lives here electrode-right/ > the > arm evolve.py steps the real RSJ dynamics sfq-pulses/ fires fill this, one Φ₀ each

Two electrode folders joined at the-dot — the witnessed . The phase difference φ lives at the dot, because the junction is the dot. Run python evolve.py and it integrates I=Ic·sinφ; push the bias past Ic and sfq-pulses/ fills with files — the neuron firing, counted on disk. browse / clone it →

The folder model isn't a toy analogy — it runs the same equations the silicon does, and it makes <• literal: a structure you can open, with firing you can list. It's the smallest honest junction, and the doorstep of the transmon.