Quantum Convolutional Neural Network: Domain-Wall Classifier

Input Spin Chain (8 qubits)

00001111

Circuit Parameters

Convolution angle θ_c 90°

Pooling angle θ_p 90°

Run

Network State

Layer

0 / 3 — 8 qubits active

P(domain wall)

—

Mean purity

1.000

How it works

An 8-qubit spin chain |ψ⟩ ∈ ℂ²⁵⁶ is prepared with basis-state flips marking "domain walls" — points where the chain switches from spin-down to spin-up. A quantum convolutional neural network (QCNN) alternates two layers to compress this into one classifying qubit:

Convolution:  U(θc) = RZZ(θc) · (RY(θc) ⊗ RY(θc))
              applied to every neighboring pair (entangles them)

Pooling:      measure control qubit → outcome m ∈ {0,1}
              apply RY(+θp) to partner if m=1, RY(−θp) if m=0
              (control is discarded, partner carries its influence forward)

Each pooling layer halves the number of active qubits: 8 → 4 → 2 → 1. After three convolution+pooling layers a single qubit remains; its Born-rule probability P(|1⟩) is the network's classification output — trained real QCNNs tune θc and θp so this probability separates chains with a domain wall from uniform chains, exactly as in Cong, Choi & Lukin's original QCNN proposal for detecting symmetry-protected topological order.

Convolution angle θc — strength of the entangling gate shared by every neighboring pair in a layer.
Pooling angle θp — how strongly the measured qubit's outcome rotates its surviving neighbor.
Mean purity — Tr(ρ²) averaged over active qubits' reduced density matrices; drops below 1 as convolution entangles qubits with the rest of the chain.

Each qubit's arrow is its true Bloch vector, computed by tracing out the other seven qubits of the real 256-amplitude statevector — not a simplified stand-in.

Active qubit Measured / traced out

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