◄ UD0   perceptron in silicon   the deep neuron   transmon
Perceptron theory · the substrate jump · classical ⇄ quantum

The perceptron in a quantum dot

Same neuron, different body. A single quantum dot hands you a perceptron's two parts almost for free: couple input gates to it and their voltages add at the dot — the weighted sum, with the coupling capacitances as the weights. And the dot only conducts when that summed charge crosses a degeneracy point — Coulomb blockade is the threshold. Weighted sum plus threshold is the whole perceptron. It's been sitting in a single electron the whole time.
weights = coupling capacitances Cᵢ  ·  inputs = gate voltages Vᵢ  ·  sum = induced charge ΣCᵢVᵢ  ·  threshold = Coulomb blockade  ·  fire = a tunnelling electron
✓ STRONG

Blockade threshold logic. Coulomb-blockade single-electron transistors and quantum-dot majority gates are fabricated, measured devices. The threshold-from-physics is real and old.

◐ MIDDLING

A single-electron perceptron net. Capacitively-summed dot neurons have been demonstrated, but they're niche and stochastic (tunnelling is probabilistic — a noisy neuron, sometimes usefully so).

◔ FRONTIER

An entangled quantum perceptron. A dot can host a qubit; a true superposition-valued perceptron ran on IBM Q (Tacchino 2019). Whether entanglement buys an advantage is open.

I · The Coulomb-blockade neuron, live

Source and drain bracket a tiny island. Two input gates and a bias gate couple to it through capacitances you set (the weights). Toggle the inputs; their gate voltages add into the island as induced charge q = b + C₁·x₁ + C₂·x₂. The island conducts — a single electron tunnels through — only when q is pushed past the blockade edge. That on/off is the neuron firing.

input x₁ input x₂
source → tunnel junction → island (the dot) → tunnel junction → drain · gates couple from below · electrons flow only when un-blockaded
0.0
induced charge q = b + ΣCᵢxᵢ
BLOCKADED
the dot conducts when q > 0 (this edge)
weighted sum= capacitive coupling threshold= Coulomb blockade output bit= a tunnelling electron
Crank a weight negative and that input pulls charge away — an inhibitory synapse, just a capacitor wired the other way. Set bias near the edge and the dot becomes a razor-sharp threshold on the sum.

II · Why the threshold is real — and secretly periodic

The blockade isn't a metaphor. Sweep the island's charge and its conductance rises and falls in Coulomb oscillations — sharp peaks at every half-integer electron (a charge state is degenerate, current flows) and dead valleys between (blockaded). The peaks need the charging energy to beat the thermal blur: E_C = e²/2C_Σ  >  ~3.5 k_BT. Raise the temperature and watch the threshold dissolve.

conductance vs induced charge (in electrons) · peaks = conduction, valleys = blockade · the violet marker is Module I's operating point
E_C charging energy
E_C / k_BT (need > ~3.5)
blockade

The honest twist: the dot's native nonlinearity is periodic, not a single sigmoid — it fires at every half-integer charge. You get a clean perceptron by operating at one edge (Module I). Used across many periods it's really a periodic-activation neuron — closer to a Fourier feature than a textbook threshold. The dot gives you more than a perceptron; the perceptron is one slice of it.

III · One dot, one cut — and depth by coupling

Because it's a linear sum through a single threshold, one dot draws exactly one straight cut across its inputs. That's enough for AND and OR — and, just like its silicon cousin, never enough for XOR. The escape is the same: couple a second dot. Two capacitively-linked dots are a quantum-dot cellular automaton majority gate — a hidden layer made of charge. Coupled dots are depth.

target:
input plane (x₁,x₂) · cyan = dot fires · the 4 cases ringed when correct for the chosen target
cases correct
one dot's verdict
AND and OR sit on one side of a single line — one dot solves them outright. XOR puts the firing corners on opposite diagonals; no single cut separates them, so one dot stalls at 3/4. Hit couple a 2nd dot and a second cut appears — the QCA majority gate carves the diagonal apart and XOR snaps to 4/4. The dendrite, the hidden layer, the coupled dot: three names for the same fold.