Create quantum_clustering.py

quantum/algorithms/quantum_clustering.py

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+# quantum_clustering.py
+import numpy as np
+from qiskit import Aer
+from qiskit.circuit import QuantumCircuit
+from qiskit.algorithms import VQE
+from qiskit.algorithms.optimizers import SLSQP
+from qiskit.primitives import Sampler
+from qiskit.quantum_info import Statevector
+from sklearn.cluster import KMeans
+
+class QuantumKMeans:
+    def __init__(self, n_clusters=2, max_iter=100, tol=1e-4):
+        """
+        Initialize the Quantum K-Means algorithm.
+
+        Parameters:
+        - n_clusters: Number of clusters to form.
+        - max_iter: Maximum number of iterations.
+        - tol: Tolerance for convergence.
+        """
+        self.n_clusters = n_clusters
+        self.max_iter = max_iter
+        self.tol = tol
+        self.centroids = None
+
+    def _quantum_state_preparation(self, data):
+        """
+        Prepare a quantum state from the data points.
+
+        Parameters:
+        - data: Input data points.
+
+        Returns:
+        - QuantumCircuit: The quantum circuit for state preparation.
+        """
+        num_qubits = int(np.ceil(np.log2(len(data))))
+        circuit = QuantumCircuit(num_qubits)
+
+        # Normalize data to prepare quantum states
+        normalized_data = data / np.linalg.norm(data)
+        for i, amplitude in enumerate(normalized_data):
+            circuit.initialize(amplitude, i)
+
+        return circuit
+
+    def _quantum_distance_measurement(self, state1, state2):
+        """
+        Measure the distance between two quantum states.
+
+        Parameters:
+        - state1: First quantum state.
+        - state2: Second quantum state.
+
+        Returns:
+        - float: The distance between the two states.
+        """
+        # Use inner product to calculate distance
+        return 1 - np.abs(np.dot(state1, state2))**2
+
+    def fit(self, data):
+        """
+        Fit the Quantum K-Means algorithm to the data.
+
+        Parameters:
+        - data: Input data points (numpy array).
+        """
+        # Initialize centroids randomly
+        random_indices = np.random.choice(len(data), self.n_clusters, replace=False)
+        self.centroids = data[random_indices]
+
+        for iteration in range(self.max_iter):
+            # Prepare quantum states for centroids
+            centroid_states = [self._quantum_state_preparation(centroid) for centroid in self.centroids]
+
+            # Assign clusters based on distance measurement
+            labels = []
+            for point in data:
+                point_state = self._quantum_state_preparation(point)
+                distances = [self._quantum_distance_measurement(point_state, centroid_state) for centroid_state in centroid_states]
+                labels.append(np.argmin(distances))
+
+            # Update centroids
+            new_centroids = np.array([data[np.array(labels) == i].mean(axis=0) for i in range(self.n_clusters)])
+
+            # Check for convergence
+            if np.all(np.abs(new_centroids - self.centroids) < self.tol):
+                break
+
+            self.centroids = new_centroids
+
+    def predict(self, data):
+        """
+        Predict the closest cluster for each data point.
+
+        Parameters:
+        - data: Input data points (numpy array).
+
+        Returns:
+        - labels: Cluster labels for each data point.
+        """
+        labels = []
+        centroid_states = [self._quantum_state_preparation(centroid) for centroid in self.centroids]
+
+        for point in data:
+            point_state = self._quantum_state_preparation(point)
+            distances = [self._quantum_distance_measurement(point_state, centroid_state) for centroid_state in centroid_states]
+            labels.append(np.argmin(distances))
+
+        return np.array(labels)
+
+if __name__ == "__main__":
+    # Example usage
+    from sklearn.datasets import make_blobs
+    import matplotlib.pyplot as plt
+
+    # Generate synthetic data
+    X, _ = make_blobs(n_samples=100, centers=3, cluster_std=0.60, random_state=0)
+
+    # Initialize and fit Quantum K-Means
+    qkmeans = QuantumKMeans(n_clusters=3)
+    qkmeans.fit(X)
+
+    # Predict clusters
+    labels = qkmeans.predict(X)
+
+    # Plot results
+    plt.scatter(X[:, 0], X[:, 1], c=labels, s=50, cmap='viridis')
+    plt.scatter(qkmeans.centroids[:, 0], qkmeans.centroids[:, 1], c='red', s=200, alpha=0.75, marker='X')
+    plt.title('Quantum K-Means Clustering')
+    plt.xlabel('Feature 1')
+    plt.ylabel('Feature 2')
+    plt.show()