Introduction to Quantum Machine Learning (QML)

Quantum Machine Learning (QML) is an emerging field that merges quantum computing and artificial intelligence (AI) to solve problems more efficiently than classical approaches.

While classical neural networks have revolutionized AI, hybrid quantum-classical neural networks (HQNNs) take advantage of quantum mechanics to potentially outperform classical models in areas like:

✅ Feature extraction in high-dimensional spaces
✅ Speeding up training for optimization-heavy models
✅ Quantum-enhanced pattern recognition

In this blog post, we will explore:

• What are hybrid quantum-classical neural networks?
• How do they improve machine learning performance?
• Implementation using Qiskit (IBM’s quantum framework) and PennyLane (a quantum machine learning library).

---

1. Understanding Hybrid Quantum-Classical Neural Networks

1.1 What Are Hybrid Neural Networks?

A Hybrid Quantum-Classical Neural Network (HQNN) is a deep learning model that combines quantum and classical computing. The typical workflow looks like this:

1. Classical Preprocessing: Convert input data into quantum-compatible formats.
2. Quantum Circuit Processing: Apply quantum gates to encode, manipulate, and process data.
3. Measurement & Post-processing: Extract quantum results and integrate them into classical models.
4. Training with Optimization: Use classical optimizers (e.g., gradient descent) to train the hybrid model.

1.2 Why Hybrid?

Quantum computers are not yet powerful enough for full-scale AI, but hybrid models allow us to leverage quantum properties for specific tasks like classification, clustering, and optimization.

---

2. Implementing a Hybrid Quantum-Classical Neural Network with Qiskit

Qiskit is IBM’s open-source quantum computing framework, widely used for quantum machine learning.

2.1 Installing Qiskit

First, install the required libraries:

pip install qiskit qiskit-machine-learning numpy 

### **2.2 Building a Quantum-Classical Neural Network in Qiskit**
import numpy as np
from qiskit import Aer, QuantumCircuit
from qiskit.circuit import Parameter
from qiskit_machine_learning.algorithms.classifiers import VQC
from qiskit_machine_learning.kernels import QuantumKernel
from qiskit.opflow import PauliSumOp
from qiskit.utils import algorithm_globals
from qiskit.algorithms.optimizers import COBYLA

# Define a quantum feature map
def feature_map():
    qc = QuantumCircuit(2)
    theta = Parameter("θ")
    qc.h([0, 1])  # Apply Hadamard gates
    qc.cx(0, 1)  # Apply CNOT gate
    qc.ry(theta, [0, 1])  # Parameterized rotation
    return qc

# Create a quantum kernel
quantum_kernel = QuantumKernel(feature_map=feature_map(), quantum_instance=Aer.get_backend("aer_simulator"))

# Training dataset (XOR classification problem)
X_train = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y_train = np.array([0, 1, 1, 0])

# Define Variational Quantum Classifier (VQC)
vqc = VQC(optimizer=COBYLA(),
          quantum_kernel=quantum_kernel,
          initial_point=[0.1, 0.2, 0.3])

# Train the model
vqc.fit(X_train, y_train)

# Test on new data
X_test = np.array([[0.5, 0.5]])
print("Prediction:", vqc.predict(X_test))