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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) |