Editing Quantum Machine Learning (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Variational quantum classifier with PennyLane:'''
<syntaxhighlight lang="python">
import pennylane as qml
import numpy as np
from pennylane import numpy as pnp

n_qubits = 4
dev = qml.device("default.qubit", wires=n_qubits)

def angle_embedding(x):
    """Encode classical data as qubit rotation angles."""
    for i, val in enumerate(x[:n_qubits]):
        qml.RY(val, wires=i)

def variational_layer(weights):
    """Trainable quantum layer."""
    for i in range(n_qubits):
        qml.RY(weights[i, 0], wires=i)
        qml.RZ(weights[i, 1], wires=i)
    # Entanglement
    for i in range(n_qubits - 1):
        qml.CNOT(wires=[i, i + 1])

@qml.qnode(dev, diff_method="parameter-shift")
def quantum_classifier(x, weights):
    angle_embedding(x)
    for layer_weights in weights:
        variational_layer(layer_weights)
    return qml.expval(qml.PauliZ(0))  # Measurement: expectation value

# Training (gradient via parameter-shift rule)
n_layers = 3
weights = pnp.random.randn(n_layers, n_qubits, 2, requires_grad=True)
opt = qml.AdamOptimizer(stepsize=0.1)

def cost(weights, X_batch, y_batch):
    preds = pnp.array([quantum_classifier(x, weights) for x in X_batch])
    return pnp.mean((preds - y_batch) ** 2)
</syntaxhighlight>

; QML approach landscape
: '''Current hardware (NISQ)''' → VQE for chemistry, QAOA for optimization, PQC classifiers
: '''Quantum annealing''' → D-Wave systems for combinatorial optimization (routing, scheduling)
: '''Quantum kernel SVM''' → Quantum feature maps + classical SVM kernel trick
: '''Future (fault-tolerant)''' → HHL for linear algebra, Grover for search, quantum PCA
: '''Hybrid classical-quantum''' → Quantum layers in PyTorch (TorchScript via PennyLane/Qiskit)
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