◄ UD0   josephson (the door)   transmon   entanglement
Perceptron theory · the eighth body · through the door, into the quantum

The perceptron in a cubi

The Josephson junction left a door open: give it a capacitor and the phase stops being a number and becomes a quantum state. That two-level state is the cubi — the qubit, in the ROOT0 tongue. Here the neuron goes fully quantum: the weights are rotations on the Bloch sphere, the input is an angle you turn the state through, and the nonlinearity arrives unbidden — the act of measuring gives P(|1⟩)=sin²(θ/2). Every other body had to find its threshold. The cubi's threshold is the wavefunction collapsing.
weights = rotations (gates)  ·  input = an encoded angle  ·  state = α|0⟩ + β|1⟩  ·  nonlinearity = the Born rule (measurement)
✓ STRONG

The cubi neuron itself. A single qubit rotated and measured — angle encoding, the Born-rule activation — is exact and runs on real quantum hardware (Tacchino et al. ran a quantum perceptron on IBM Q, 2019).

◐ MIDDLING

Variational quantum classifiers. Small quantum neural nets are demonstrated, but it's the NISQ era — noise, decoherence, and barren plateaus (vanishing gradients) make training hard at scale.

◔ FRONTIER

Quantum advantage for learning. Whether a quantum model actually beats a classical one on real data is open and genuinely contested — the honest line between physics and hype.

I · The cubi, and measurement as the nonlinearity

A cubi's state is a point on the Bloch sphere: north pole is |0⟩, south is |1⟩, and everywhere between is a superposition α|0⟩ + e^{iφ}β|1⟩. The weights and inputs are rotations — they turn the arrow. But you never read α and β directly; you measure, and the state collapses to |0⟩ or |1⟩ with probability P(|1⟩) = sin²(θ/2) That curve — 0 at the north pole, ½ at the equator, 1 at the south — is a built-in nonlinear activation. The measurement is the neuron.

the Bloch sphere · the cubi state arrow · |0⟩ north, |1⟩ south · measuring snaps it to a pole
0.87|0⟩ + 0.50|1⟩
amplitudes α, β
P(1) = 0.25
the activation = sin²(θ/2)
measured tally — converges to the Born probabilities
Before measuring, the cubi is both — the activation exists as an amplitude, undecided. Measuring forces a 0 or a 1, biased by sin²(θ/2). Run it many times and the average is the smooth activation; run it once and you get a quantum coin flip. The nonlinearity and the randomness are the same act.

II · The cubi perceptron — rotate by the weighted sum, then measure

Encode the inputs as rotation angles and the weights as how hard each one turns the cubi. The rotations compose — the state ends at θ = b + Σ wᵢxᵢ — and the Born rule reads out the activation P(|1⟩) = sin²(θ/2). Threshold it (more likely |1⟩ than |0⟩) and the cubi fires. It's the same weighted-sum-then-squash as every body — except the squash is physics you can't avoid.

x₁ x₂
the cubi rotated to θ = b + Σwᵢxᵢ · its latitude sets P(|1⟩) · cross the equator → fires
θ = 0°
accumulated rotation
P(1) = 0.50
Born activation
|0⟩ — dark
fires when P(1) > ½
multiply/sum= composed rotationsactivation= the Born rulereadout= a measurement

III · It learns — and entanglement is the new depth

Train the rotation angles and the cubi learns AND/OR in a few sweeps. One cubi, encoded linearly, is still one cutXOR stalls at 3/4 (verified), exactly like its seven classical cousins. But the quantum world has a different escape than stacking layers: a feature map that entangles the inputs adds an x₁·x₂ cross-term, lifting the data into a space where XOR is separable. Flip ⊗ entangle and XOR snaps to 4/4. Entanglement does what depth did — that's the quantum twist on the oldest wall in the series.

target:
press train

The honest line (this is the contested one). The cubi's mechanism is real and runs on real hardware. The feature map lifting XOR is exactly how quantum kernels work, and it's genuinely quantum. But whether this buys a real-world advantage over a classical net — once you account for noise, the cost of loading data into amplitudes, and reading it back out — is unsettled and hotly argued. The physics is sound; the supremacy is a promissory note. We mark it FRONTIER on purpose.

the cubi's gift= measurement is the activation the cubi's depth= entanglement, not more layers the cubi's caveat= advantage unproven (NISQ)

This is where the road that began in a branch predictor arrives: the dot product turned into a quantum amplitude, the threshold into a measurement, depth into entanglement. Same neuron, eighth body — and the first one that is genuinely uncertain about its own answer until you look.

silicon · cortical · quantum dot · light · crossbar · spin · josephson · cubi  —  one neuron, eight bodies