Quantum Neural Networks (QNN) Architecture & High-Dimensional Representations

Quantum Neural Networks (QNNs) merge quantum computing circuits with deep learning principles. By encoding classical data into quantum Hilbert space, QNNs exploit superposition and entanglement to model non-linear data distributions that classical neural networks struggle to process efficiently.

Core Mechanisms

1. Quantum Data Encoding: Amplitude or angle encoding to represent feature vectors as quantum states.
2. Parameterized Quantum Layers: Unitary transformations acting as trainable weights.
3. Quantum Measurements & Loss Computation: Expectation value measurement followed by gradient updates via the Parameter-Shift rule.

# Parameterized QNN Layer Definition
def qnn_layer(weights, wires):
    for i, wire in enumerate(wires):
        qml.Rot(*weights[i], wires=wire)
    for i in range(len(wires) - 1):
        qml.CNOT(wires=[wires[i], wires[i + 1]])