import numpy as np
from typing import List, Tuple

class ChernSimonsTopology:
    def __init__(self, depth: int):
        self.depth = depth
        self.dimension = 2 ** depth
        self.connections = self._initialize_connections()
        
    def _initialize_connections(self) -> List[Tuple[int, int]]:
        """Initialize topological connections based on Chern-Simons theory"""
        connections = []
        for i in range(self.depth - 1):
            for j in range(i + 1, self.depth):
                connections.append((i, j))
        return connections
        
    def get_allowed_operations(self, qubit: int) -> List[str]:
        """Get allowed quantum operations for given qubit"""
        if 0 <= qubit < self.depth:
            return ["H", "X", "Z", "Phase"]
        return []
        
    def calculate_braiding(self, q1: int, q2: int) -> np.ndarray:
        """Calculate braiding operation between two qubits"""
        if (q1, q2) in self.connections or (q2, q1) in self.connections:
            theta = np.pi / 4  # Topological phase
            c = np.cos(theta)
            s = np.sin(theta)
            return np.array([[c, -s, 0, 0],
                           [s, c, 0, 0],
                           [0, 0, c, -s],
                           [0, 0, s, c]])
        return np.eye(4)