Add Quantum k-Means Clustering Implementation

quantum/quantum_kmeans_clustering.py

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+import cirq
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.datasets import make_blobs
+from sklearn.preprocessing import MinMaxScaler
+
+def generate_data(n_samples=100, n_features=2, n_clusters=2):
+    data, labels = make_blobs(n_samples=n_samples, centers=n_clusters, n_features=n_features, random_state=42)
+    return MinMaxScaler().fit_transform(data), labels
+
+def quantum_distance(point1, point2):
+    """
+    Quantum circuit explanation:
+    1. Use a single qubit to encode the distance between two points.
+    2. Apply Ry rotation based on the normalized Euclidean distance.
+    3. Measure the qubit to get a probabilistic distance metric.
+    The probability of measuring |1> correlates with the distance between points.
+    """
+    qubit = cirq.LineQubit(0)
+    diff = np.clip(np.linalg.norm(point1 - point2), 0, 1)
+    theta = 2 * np.arcsin(diff)
+
+    circuit = cirq.Circuit(
+        cirq.ry(theta)(qubit),
+        cirq.measure(qubit, key='result')
+    )
+
+    result = cirq.Simulator().run(circuit, repetitions=1000)
+    return result.histogram(key='result').get(1, 0) / 1000
+
+def initialize_centroids(data, k):
+    return data[np.random.choice(len(data), k, replace=False)]
+
+def assign_clusters(data, centroids):
+    clusters = [[] for _ in range(len(centroids))]
+    for point in data:
+        closest = min(range(len(centroids)), key=lambda i: quantum_distance(point, centroids[i]))
+        clusters[closest].append(point)
+    return clusters
+
+def recompute_centroids(clusters):
+    return np.array([np.mean(cluster, axis=0) for cluster in clusters if cluster])
+
+def quantum_kmeans(data, k, max_iters=10):
+    centroids = initialize_centroids(data, k)
+
+    for _ in range(max_iters):
+        clusters = assign_clusters(data, centroids)
+        new_centroids = recompute_centroids(clusters)
+        if np.allclose(new_centroids, centroids):
+            break
+        centroids = new_centroids
+
+    return centroids, clusters
+
+# Main execution
+n_samples, n_clusters = 10, 2
+data, labels = generate_data(n_samples, n_clusters=n_clusters)
+
+plt.figure(figsize=(12, 5))
+
+plt.subplot(121)
+plt.scatter(data[:, 0], data[:, 1], c=labels)
+plt.title("Generated Data")
+
+final_centroids, final_clusters = quantum_kmeans(data, n_clusters)
+
+plt.subplot(122)
+for i, cluster in enumerate(final_clusters):
+    cluster = np.array(cluster)
+    plt.scatter(cluster[:, 0], cluster[:, 1], label=f'Cluster {i+1}')
+plt.scatter(final_centroids[:, 0], final_centroids[:, 1], color='red', marker='x', s=200, linewidths=3, label='Centroids')
+plt.title("Quantum k-Means Clustering with Cirq")
+plt.legend()
+
+plt.tight_layout()
+plt.show()
+
+print(f"Final Centroids:\n{final_centroids}")