| 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
|
| 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) |
