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