Objective

To implement a hybrid quantum-classical model that can classify simple datasets (such as an MNIST subset or the Iris dataset). The Variational Quantum Classifier (VQC) combines quantum circuits with classical optimization to achieve effective classification on NISQ devices.

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Concept Recap

• Data Encoding → Translate classical features into quantum states.
• Variational Circuit (Ansatz) → A parameterized quantum neural network.
• Classical Optimizer → Adjusts parameters using gradient-based methods.
• Evaluation → Compare accuracy with classical baselines like Logistic Regression or SVM.

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Implementation Steps

Step 1: Encode Data into Quantum States

• Classical data (e.g., Iris petal lengths, MNIST pixels) must be mapped into qubits.
• Encoding methods:
  • Angle Encoding → Use features as rotation angles.
  • Amplitude Encoding → Use amplitudes of quantum states (efficient, but harder).

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Step 2: Design a Parameterized Quantum Circuit

• Build an ansatz with:
  • Rotation gates (Rx, Ry, Rz).
  • Entangling gates (CNOT).
• Depth of the circuit balances expressivity vs noise resilience.

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Step 3: Train with a Classical Optimizer

• Define a loss function (e.g., cross-entropy).
• Use optimizers like:
  • Gradient Descent
  • Adam
  • SPSA (Simultaneous Perturbation Stochastic Approximation, good for noisy devices).

Training loop:

1. Forward pass → Run quantum circuit.
2. Measure expectation values → Map to prediction.
3. Compute loss.
4. Update parameters via optimizer.

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Step 4: Evaluate Performance Against Classical Models

• Train a baseline classifier (e.g., Logistic Regression, SVM, Neural Network).
• Compare:
  • Accuracy
  • Training time
  • Resource efficiency
• Highlight scenarios where quantum classifiers may generalize better on small/noisy datasets.

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Mini Example (PennyLane + Iris Dataset)

import pennylane as qml
from pennylane import numpy as np
from sklearn.datasets import load_iris
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split

# Load Iris dataset (2 classes for simplicity)
iris = load_iris()
X = iris.data[iris.target != 2][:, :2]   # 2D features
Y = iris.target[iris.target != 2] * 2 - 1   # map {0,1} → {-1,1}
X = StandardScaler().fit_transform(X)
X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.2)

# Quantum device
dev = qml.device("default.qubit", wires=2)

# Ansatz circuit
def circuit(x, params):
    qml.AngleEmbedding(x, wires=[0, 1])
    qml.StronglyEntanglingLayers(params, wires=[0, 1])
    return qml.expval(qml.PauliZ(0))

@qml.qnode(dev)
def vqc(x, params):
    return circuit(x, params)

# Loss function
def cost(params, X, Y):
    preds = [vqc(x, params) for x in X]
    return np.mean((np.array(preds) - Y) ** 2)

# Training
params = np.random.random((1, 2, 3))
opt = qml.AdamOptimizer(stepsize=0.1)

for epoch in range(30):
    params, loss = opt.step_and_cost(lambda p: cost(p, X_train, Y_train), params)
    if epoch % 5 == 0:
        print(f"Epoch {epoch}: Loss = {loss:.4f}")

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Applications

• Classifying small image datasets (MNIST subset)
• Identifying species in Iris dataset
• Fraud detection (binary classification)
• Disease classification (genomics/healthcare)

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Key Takeaways

• VQCs combine quantum circuits + classical training loops.
• Useful for small, noisy datasets on NISQ devices.
• Performance should always be compared with classical baselines.

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➡️ Next: Hybrid Model: Classical Preprocessing + Quantum Classifier