""" Copied from Anders' original C++ implementation S. Anders, H. J. Briegel: Fast Simulation of Stabilizer Circuits using a Graph State Formalism quant-ph/0504117 """ from __future__ import absolute_import import numpy as np cz_table = ((((1, 0, 0), (1, 0, 0), (1, 0, 3), (1, 0, 3), (1, 0, 5), (1, 0, 5), (1, 0, 6), (1, 0, 6), (0, 3, 8), (0, 3, 8), (0, 0, 10), (0, 0, 10), (1, 0, 3), (1, 0, 3), (1, 0, 0), (1, 0, 0), (1, 0, 6), (1, 0, 6), (1, 0, 5), (1, 0, 5), (0, 0, 10), (0, 0, 10), (0, 3, 8), (0, 3, 8)), ((1, 0, 0), (1, 0, 0), (1, 0, 3), (1, 0, 3), (1, 0, 5), (1, 0, 5), (1, 0, 6), (1, 0, 6), (0, 2, 8), (0, 2, 8), (0, 0, 10), (0, 0, 10), (1, 0, 3), (1, 0, 3), (1, 0, 0), (1, 0, 0), (1, 0, 6), (1, 0, 6), (1, 0, 5), (1, 0, 5), (0, 0, 10), (0, 0, 10), (0, 2, 8), (0, 2, 8)), ((1, 2, 3), (1, 0, 1), (1, 0, 2), (1, 2, 0), (1, 0, 4), (1, 2, 6), (1, 2, 5), (1, 0, 7), (0, 0, 8), (0, 0, 8), (0, 2, 10), (0, 2, 10), (1, 0, 2), (1, 0, 2), (1, 0, 1), (1, 0, 1), (1, 0, 7), (1, 0, 7), (1, 0, 4), (1, 0, 4), (0, 2, 10), (0, 2, 10), (0, 0, 8), (0, 0, 8)), ((1, 3, 0), (1, 0, 1), (1, 0, 2), (1, 3, 3), (1, 0, 4), (1, 3, 5), (1, 3, 6), (1, 0, 7), (0, 0, 8), (0, 0, 8), (0, 3, 10), (0, 3, 10), (1, 0, 2), (1, 0, 2), (1, 0, 1), (1, 0, 1), (1, 0, 7), (1, 0, 7), (1, 0, 4), (1, 0, 4), (0, 3, 10), (0, 3, 10), (0, 0, 8), (0, 0, 8)), ((1, 4, 3), (1, 4, 3), (1, 4, 0), (1, 4, 0), (1, 4, 6), (1, 4, 6), (1, 4, 5), (1, 4, 5), (0, 6, 8), (0, 6, 8), (0, 4, 10), (0, 4, 10), (1, 4, 0), (1, 4, 0), (1, 4, 3), (1, 4, 3), (1, 4, 5), (1, 4, 5), (1, 4, 6), (1, 4, 6), (0, 4, 10), (0, 4, 10), (0, 6, 8), (0, 6, 8)), ((1, 5, 0), (1, 5, 0), (1, 5, 3), (1, 5, 3), (1, 5, 5), (1, 5, 5), (1, 5, 6), (1, 5, 6), (0, 6, 8), (0, 6, 8), (0, 5, 10), (0, 5, 10), (1, 5, 3), (1, 5, 3), (1, 5, 0), (1, 5, 0), (1, 5, 6), (1, 5, 6), (1, 5, 5), (1, 5, 5), (0, 5, 10), (0, 5, 10), (0, 6, 8), (0, 6, 8)), ((1, 6, 0), (1, 5, 1), (1, 5, 2), (1, 6, 3), (1, 5, 4), (1, 6, 5), (1, 6, 6), (1, 5, 7), (0, 5, 8), (0, 5, 8), (0, 6, 10), (0, 6, 10), (1, 5, 2), (1, 5, 2), (1, 5, 1), (1, 5, 1), (1, 5, 7), (1, 5, 7), (1, 5, 4), (1, 5, 4), (0, 6, 10), (0, 6, 10), (0, 5, 8), (0, 5, 8)), ((1, 6, 0), (1, 4, 2), (1, 4, 1), (1, 6, 3), (1, 4, 7), (1, 6, 5), (1, 6, 6), (1, 4, 4), (0, 4, 8), (0, 4, 8), (0, 6, 10), (0, 6, 10), (1, 4, 1), (1, 4, 1), (1, 4, 2), (1, 4, 2), (1, 4, 4), (1, 4, 4), (1, 4, 7), (1, 4, 7), (0, 6, 10), (0, 6, 10), (0, 4, 8), (0, 4, 8)), ((0, 8, 3), (0, 8, 2), (0, 8, 0), (0, 8, 0), (0, 8, 6), (0, 8, 6), (0, 8, 5), (0, 8, 4), (0, 8, 8), (0, 8, 8), (0, 8, 10), (0, 8, 10), (0, 8, 0), (0, 8, 0), (0, 8, 2), (0, 8, 2), (0, 8, 4), (0, 8, 4), (0, 8, 6), (0, 8, 6), (0, 8, 10), (0, 8, 10), (0, 8, 8), (0, 8, 8)), ((0, 8, 3), (0, 8, 2), (0, 8, 0), (0, 8, 0), (0, 8, 6), (0, 8, 6), (0, 8, 5), (0, 8, 4), (0, 8, 8), (0, 8, 8), (0, 8, 10), (0, 8, 10), (0, 8, 0), (0, 8, 0), (0, 8, 2), (0, 8, 2), (0, 8, 4), (0, 8, 4), (0, 8, 6), (0, 8, 6), (0, 8, 10), (0, 8, 10), (0, 8, 8), (0, 8, 8)), ((0, 10, 0), (0, 10, 0), (0, 10, 2), (0, 10, 3), (0, 10, 4), (0, 10, 5), (0, 10, 6), (0, 10, 6), (0, 10, 8), (0, 10, 8), (0, 10, 10), (0, 10, 10), (0, 10, 2), (0, 10, 2), (0, 10, 0), (0, 10, 0), (0, 10, 6), (0, 10, 6), (0, 10, 4), (0, 10, 4), (0, 10, 10), (0, 10, 10), (0, 10, 8), (0, 10, 8)), ((0, 10, 0), (0, 10, 0), (0, 10, 2), (0, 10, 3), (0, 10, 4), (0, 10, 5), (0, 10, 6), (0, 10, 6), (0, 10, 8), (0, 10, 8), (0, 10, 10), (0, 10, 10), (0, 10, 2), (0, 10, 2), (0, 10, 0), (0, 10, 0), (0, 10, 6), (0, 10, 6), (0, 10, 4), (0, 10, 4), (0, 10, 10), (0, 10, 10), (0, 10, 8), (0, 10, 8)), ((1, 2, 3), (1, 0, 1), (1, 0, 2), (1, 2, 0), (1, 0, 4), (1, 2, 6), (1, 2, 5), (1, 0, 7), (0, 0, 8), (0, 0, 8), (0, 2, 10), (0, 2, 10), (1, 0, 2), (1, 0, 2), (1, 0, 1), (1, 0, 1), (1, 0, 7), (1, 0, 7), (1, 0, 4), (1, 0, 4), (0, 2, 10), (0, 2, 10), (0, 0, 8), (0, 0, 8)), ((1, 2, 3), (1, 0, 1), (1, 0, 2), (1, 2, 0), (1, 0, 4), (1, 2, 6), (1, 2, 5), (1, 0, 7), (0, 0, 8), (0, 0, 8), (0, 2, 10), (0, 2, 10), (1, 0, 2), (1, 0, 2), (1, 0, 1), (1, 0, 1), (1, 0, 7), (1, 0, 7), (1, 0, 4), (1, 0, 4), (0, 2, 10), (0, 2, 10), (0, 0, 8), (0, 0, 8)), ((1, 0, 0), (1, 0, 0), (1, 0, 3), (1, 0, 3), (1, 0, 5), (1, 0, 5), (1, 0, 6), (1, 0, 6), (0, 2, 8), (0, 2, 8), (0, 0, 10), (0, 0, 10), (1, 0, 3), (1, 0, 3), (1, 0, 0), (1, 0, 0), (1, 0, 6), (1, 0, 6), (1, 0, 5), (1, 0, 5), (0, 0, 10), (0, 0, 10), (0, 2, 8), (0, 2, 8)), ((1, 0, 0), (1, 0, 0), (1, 0, 3), (1, 0, 3), (1, 0, 5), (1, 0, 5), (1, 0, 6), (1, 0, 6), (0, 2, 8), (0, 2, 8), (0, 0, 10), (0, 0, 10), (1, 0, 3), (1, 0, 3), (1, 0, 0), (1, 0, 0), (1, 0, 6), (1, 0, 6), (1, 0, 5), (1, 0, 5), (0, 0, 10), (0, 0, 10), (0, 2, 8), (0, 2, 8)), ((1, 6, 0), (1, 4, 2), (1, 4, 1), (1, 6, 3), (1, 4, 7), (1, 6, 5), (1, 6, 6), (1, 4, 4), (0, 4, 8), (0, 4, 8), (0, 6, 10), (0, 6, 10), (1, 4, 1), (1, 4, 1), (1, 4, 2), (1, 4, 2), (1, 4, 4), (1, 4, 4), (1, 4, 7), (1, 4, 7), (0, 6, 10), (0, 6, 10), (0, 4, 8), (0, 4, 8)), ((1, 6, 0), (1, 4, 2), (1, 4, 1), (1, 6, 3), (1, 4, 7), (1, 6, 5), (1, 6, 6), (1, 4, 4), (0, 4, 8), (0, 4, 8), (0, 6, 10), (0, 6, 10), (1, 4, 1), (1, 4, 1), (1, 4, 2), (1, 4, 2), (1, 4, 4), (1, 4, 4), (1, 4, 7), (1, 4, 7), (0, 6, 10), (0, 6, 10), (0, 4, 8), (0, 4, 8)), ((1, 4, 3), (1, 4, 3), (1, 4, 0), (1, 4, 0), (1, 4, 6), (1, 4, 6), (1, 4, 5), (1, 4, 5), (0, 6, 8), (0, 6, 8), (0, 4, 10), (0, 4, 10), (1, 4, 0), (1, 4, 0), (1, 4, 3), (1, 4, 3), (1, 4, 5), (1, 4, 5), (1, 4, 6), (1, 4, 6), (0, 4, 10), (0, 4, 10), (0, 6, 8), (0, 6, 8)), ((1, 4, 3), (1, 4, 3), (1, 4, 0), (1, 4, 0), (1, 4, 6), (1, 4, 6), (1, 4, 5), (1, 4, 5), (0, 6, 8), (0, 6, 8), (0, 4, 10), (0, 4, 10), (1, 4, 0), (1, 4, 0), (1, 4, 3), (1, 4, 3), (1, 4, 5), (1, 4, 5), (1, 4, 6), (1, 4, 6), (0, 4, 10), (0, 4, 10), (0, 6, 8), (0, 6, 8)), ((0, 10, 0), (0, 10, 0), (0, 10, 2), (0, 10, 3), (0, 10, 4), (0, 10, 5), (0, 10, 6), (0, 10, 6), (0, 10, 8), (0, 10, 8), (0, 10, 10), (0, 10, 10), (0, 10, 2), (0, 10, 2), (0, 10, 0), (0, 10, 0), (0, 10, 6), (0, 10, 6), (0, 10, 4), (0, 10, 4), (0, 10, 10), (0, 10, 10), (0, 10, 8), (0, 10, 8)), ((0, 10, 0), (0, 10, 0), (0, 10, 2), (0, 10, 3), (0, 10, 4), (0, 10, 5), (0, 10, 6), (0, 10, 6), (0, 10, 8), (0, 10, 8), (0, 10, 10), (0, 10, 10), (0, 10, 2), (0, 10, 2), (0, 10, 0), (0, 10, 0), (0, 10, 6), (0, 10, 6), (0, 10, 4), (0, 10, 4), (0, 10, 10), (0, 10, 10), (0, 10, 8), (0, 10, 8)), ((0, 8, 3), (0, 8, 2), (0, 8, 0), (0, 8, 0), (0, 8, 6), (0, 8, 6), (0, 8, 5), (0, 8, 4), (0, 8, 8), (0, 8, 8), (0, 8, 10), (0, 8, 10), (0, 8, 0), (0, 8, 0), (0, 8, 2), (0, 8, 2), (0, 8, 4), (0, 8, 4), (0, 8, 6), (0, 8, 6), (0, 8, 10), (0, 8, 10), (0, 8, 8), (0, 8, 8)), ((0, 8, 3), (0, 8, 2), (0, 8, 0), (0, 8, 0), (0, 8, 6), (0, 8, 6), (0, 8, 5), (0, 8, 4), (0, 8, 8), (0, 8, 8), (0, 8, 10), (0, 8, 10), (0, 8, 0), (0, 8, 0), (0, 8, 2), (0, 8, 2), (0, 8, 4), (0, 8, 4), (0, 8, 6), (0, 8, 6), (0, 8, 10), (0, 8, 10), (0, 8, 8), (0, 8, 8))), (((0, 0, 0), (0, 3, 0), (0, 3, 2), (0, 0, 3), (0, 3, 4), (0, 0, 5), (0, 0, 6), (0, 3, 6), (1, 5, 23), (1, 5, 22), (1, 5, 21), (1, 5, 20), (0, 5, 2), (0, 6, 2), (0, 5, 0), (0, 6, 0), (0, 6, 6), (0, 5, 6), (0, 6, 4), (0, 5, 4), (1, 5, 10), (1, 5, 11), (1, 5, 8), (1, 5, 9)), ((0, 0, 3), (0, 2, 2), (0, 2, 0), (0, 0, 0), (0, 2, 6), (0, 0, 6), (0, 0, 5), (0, 2, 4), (1, 4, 23), (1, 4, 22), (1, 4, 21), (1, 4, 20), (0, 6, 0), (0, 4, 0), (0, 6, 2), (0, 4, 2), (0, 4, 4), (0, 6, 4), (0, 4, 6), (0, 6, 6), (1, 4, 10), (1, 4, 11), (1, 4, 8), (1, 4, 9)), ((0, 2, 3), (0, 0, 2), (0, 0, 0), (0, 2, 0), (0, 0, 6), (0, 2, 6), (0, 2, 5), (0, 0, 4), (1, 4, 22), (1, 4, 23), (1, 4, 20), (1, 4, 21), (0, 4, 0), (0, 6, 0), (0, 4, 2), (0, 6, 2), (0, 6, 4), (0, 4, 4), (0, 6, 6), (0, 4, 6), (1, 4, 11), (1, 4, 10), (1, 4, 9), (1, 4, 8)), ((0, 3, 0), (0, 0, 0), (0, 0, 2), (0, 3, 3), (0, 0, 4), (0, 3, 5), (0, 3, 6), (0, 0, 6), (1, 5, 22), (1, 5, 23), (1, 5, 20), (1, 5, 21), (0, 6, 2), (0, 5, 2), (0, 6, 0), (0, 5, 0), (0, 5, 6), (0, 6, 6), (0, 5, 4), (0, 6, 4), (1, 5, 11), (1, 5, 10), (1, 5, 9), (1, 5, 8)), ((0, 4, 3), (0, 6, 2), (0, 6, 0), (0, 4, 0), (0, 6, 6), (0, 4, 6), (0, 4, 5), (0, 6, 4), (1, 0, 21), (1, 0, 20), (1, 0, 23), (1, 0, 22), (0, 0, 0), (0, 2, 0), (0, 0, 2), (0, 2, 2), (0, 2, 4), (0, 0, 4), (0, 2, 6), (0, 0, 6), (1, 0, 8), (1, 0, 9), (1, 0, 10), (1, 0, 11)), ((0, 5, 0), (0, 6, 0), (0, 6, 2), (0, 5, 3), (0, 6, 4), (0, 5, 5), (0, 5, 6), (0, 6, 6), (1, 0, 22), (1, 0, 23), (1, 0, 20), (1, 0, 21), (0, 3, 2), (0, 0, 2), (0, 3, 0), (0, 0, 0), (0, 0, 6), (0, 3, 6), (0, 0, 4), (0, 3, 4), (1, 0, 11), (1, 0, 10), (1, 0, 9), (1, 0, 8)), ((0, 6, 0), (0, 5, 0), (0, 5, 2), (0, 6, 3), (0, 5, 4), (0, 6, 5), (0, 6, 6), (0, 5, 6), (1, 0, 23), (1, 0, 22), (1, 0, 21), (1, 0, 20), (0, 0, 2), (0, 3, 2), (0, 0, 0), (0, 3, 0), (0, 3, 6), (0, 0, 6), (0, 3, 4), (0, 0, 4), (1, 0, 10), (1, 0, 11), (1, 0, 8), (1, 0, 9)), ((0, 6, 3), (0, 4, 2), (0, 4, 0), (0, 6, 0), (0, 4, 6), (0, 6, 6), (0, 6, 5), (0, 4, 4), (1, 0, 20), (1, 0, 21), (1, 0, 22), (1, 0, 23), (0, 2, 0), (0, 0, 0), (0, 2, 2), (0, 0, 2), (0, 0, 4), (0, 2, 4), (0, 0, 6), (0, 2, 6), (1, 0, 9), (1, 0, 8), (1, 0, 11), (1, 0, 10)), ((1, 22, 6), (1, 20, 5), (1, 20, 6), (1, 22, 5), (1, 20, 3), (1, 22, 0), (1, 22, 3), (1, 20, 0), (0, 0, 0), (0, 0, 2), (0, 2, 2), (0, 2, 0), (0, 6, 6), (0, 4, 4), (0, 6, 4), (0, 4, 6), (0, 4, 2), (0, 6, 0), (0, 4, 0), (0, 6, 2), (0, 2, 4), (0, 2, 6), (0, 0, 6), (0, 0, 4)), ((1, 22, 5), (1, 20, 6), (1, 20, 5), (1, 22, 6), (1, 20, 0), (1, 22, 3), (1, 22, 0), (1, 20, 3), (0, 2, 0), (0, 2, 2), (0, 0, 2), (0, 0, 0), (0, 4, 6), (0, 6, 4), (0, 4, 4), (0, 6, 6), (0, 6, 2), (0, 4, 0), (0, 6, 0), (0, 4, 2), (0, 0, 4), (0, 0, 6), (0, 2, 6), (0, 2, 4)), ((1, 20, 6), (1, 20, 7), (1, 20, 4), (1, 20, 5), (1, 20, 1), (1, 20, 0), (1, 20, 3), (1, 20, 2), (0, 2, 2), (0, 2, 0), (0, 0, 0), (0, 0, 2), (0, 6, 4), (0, 4, 6), (0, 6, 6), (0, 4, 4), (0, 4, 0), (0, 6, 2), (0, 4, 2), (0, 6, 0), (0, 0, 6), (0, 0, 4), (0, 2, 4), (0, 2, 6)), ((1, 20, 5), (1, 20, 4), (1, 20, 7), (1, 20, 6), (1, 20, 2), (1, 20, 3), (1, 20, 0), (1, 20, 1), (0, 0, 2), (0, 0, 0), (0, 2, 0), (0, 2, 2), (0, 4, 4), (0, 6, 6), (0, 4, 6), (0, 6, 4), (0, 6, 0), (0, 4, 2), (0, 6, 2), (0, 4, 0), (0, 2, 6), (0, 2, 4), (0, 0, 4), (0, 0, 6)), ((0, 2, 5), (0, 0, 6), (0, 0, 4), (0, 2, 6), (0, 0, 0), (0, 2, 3), (0, 2, 0), (0, 0, 2), (0, 6, 6), (0, 6, 4), (0, 4, 6), (0, 4, 4), (1, 16, 18), (1, 16, 19), (1, 16, 16), (1, 16, 17), (1, 16, 12), (1, 16, 13), (1, 16, 14), (1, 16, 15), (0, 4, 2), (0, 4, 0), (0, 6, 2), (0, 6, 0)), ((0, 2, 6), (0, 0, 4), (0, 0, 6), (0, 2, 5), (0, 0, 2), (0, 2, 0), (0, 2, 3), (0, 0, 0), (0, 4, 4), (0, 4, 6), (0, 6, 4), (0, 6, 6), (1, 16, 17), (1, 16, 16), (1, 16, 19), (1, 16, 18), (1, 16, 15), (1, 16, 14), (1, 16, 13), (1, 16, 12), (0, 6, 0), (0, 6, 2), (0, 4, 0), (0, 4, 2)), ((0, 0, 5), (0, 2, 6), (0, 2, 4), (0, 0, 6), (0, 2, 0), (0, 0, 3), (0, 0, 0), (0, 2, 2), (0, 4, 6), (0, 4, 4), (0, 6, 6), (0, 6, 4), (1, 16, 16), (1, 16, 17), (1, 16, 18), (1, 16, 19), (1, 16, 14), (1, 16, 15), (1, 16, 12), (1, 16, 13), (0, 6, 2), (0, 6, 0), (0, 4, 2), (0, 4, 0)), ((0, 0, 6), (0, 2, 4), (0, 2, 6), (0, 0, 5), (0, 2, 2), (0, 0, 0), (0, 0, 3), (0, 2, 0), (0, 6, 4), (0, 6, 6), (0, 4, 4), (0, 4, 6), (1, 16, 19), (1, 16, 18), (1, 16, 17), (1, 16, 16), (1, 16, 13), (1, 16, 12), (1, 16, 15), (1, 16, 14), (0, 4, 0), (0, 4, 2), (0, 6, 0), (0, 6, 2)), ((0, 6, 6), (0, 4, 4), (0, 4, 6), (0, 6, 5), (0, 4, 2), (0, 6, 0), (0, 6, 3), (0, 4, 0), (0, 2, 4), (0, 2, 6), (0, 0, 4), (0, 0, 6), (1, 12, 16), (1, 12, 17), (1, 12, 18), (1, 12, 19), (1, 12, 14), (1, 12, 15), (1, 12, 12), (1, 12, 13), (0, 0, 0), (0, 0, 2), (0, 2, 0), (0, 2, 2)), ((0, 6, 5), (0, 4, 6), (0, 4, 4), (0, 6, 6), (0, 4, 0), (0, 6, 3), (0, 6, 0), (0, 4, 2), (0, 0, 6), (0, 0, 4), (0, 2, 6), (0, 2, 4), (1, 12, 19), (1, 12, 18), (1, 12, 17), (1, 12, 16), (1, 12, 13), (1, 12, 12), (1, 12, 15), (1, 12, 14), (0, 2, 2), (0, 2, 0), (0, 0, 2), (0, 0, 0)), ((0, 4, 6), (0, 6, 4), (0, 6, 6), (0, 4, 5), (0, 6, 2), (0, 4, 0), (0, 4, 3), (0, 6, 0), (0, 0, 4), (0, 0, 6), (0, 2, 4), (0, 2, 6), (1, 12, 18), (1, 12, 19), (1, 12, 16), (1, 12, 17), (1, 12, 12), (1, 12, 13), (1, 12, 14), (1, 12, 15), (0, 2, 0), (0, 2, 2), (0, 0, 0), (0, 0, 2)), ((0, 4, 5), (0, 6, 6), (0, 6, 4), (0, 4, 6), (0, 6, 0), (0, 4, 3), (0, 4, 0), (0, 6, 2), (0, 2, 6), (0, 2, 4), (0, 0, 6), (0, 0, 4), (1, 12, 17), (1, 12, 16), (1, 12, 19), (1, 12, 18), (1, 12, 15), (1, 12, 14), (1, 12, 13), (1, 12, 12), (0, 0, 2), (0, 0, 0), (0, 2, 2), (0, 2, 0)), ((1, 10, 5), (1, 8, 6), (1, 8, 5), (1, 10, 6), (1, 8, 0), (1, 10, 3), (1, 10, 0), (1, 8, 3), (0, 4, 2), (0, 4, 0), (0, 6, 0), (0, 6, 2), (0, 2, 4), (0, 0, 6), (0, 2, 6), (0, 0, 4), (0, 0, 0), (0, 2, 2), (0, 0, 2), (0, 2, 0), (0, 6, 6), (0, 6, 4), (0, 4, 4), (0, 4, 6)), ((1, 10, 6), (1, 8, 5), (1, 8, 6), (1, 10, 5), (1, 8, 3), (1, 10, 0), (1, 10, 3), (1, 8, 0), (0, 6, 2), (0, 6, 0), (0, 4, 0), (0, 4, 2), (0, 0, 4), (0, 2, 6), (0, 0, 6), (0, 2, 4), (0, 2, 0), (0, 0, 2), (0, 2, 2), (0, 0, 0), (0, 4, 6), (0, 4, 4), (0, 6, 4), (0, 6, 6)), ((1, 8, 5), (1, 8, 4), (1, 8, 7), (1, 8, 6), (1, 8, 2), (1, 8, 3), (1, 8, 0), (1, 8, 1), (0, 6, 0), (0, 6, 2), (0, 4, 2), (0, 4, 0), (0, 2, 6), (0, 0, 4), (0, 2, 4), (0, 0, 6), (0, 0, 2), (0, 2, 0), (0, 0, 0), (0, 2, 2), (0, 4, 4), (0, 4, 6), (0, 6, 6), (0, 6, 4)), ((1, 8, 6), (1, 8, 7), (1, 8, 4), (1, 8, 5), (1, 8, 1), (1, 8, 0), (1, 8, 3), (1, 8, 2), (0, 4, 0), (0, 4, 2), (0, 6, 2), (0, 6, 0), (0, 0, 6), (0, 2, 4), (0, 0, 4), (0, 2, 6), (0, 2, 2), (0, 0, 0), (0, 2, 0), (0, 0, 2), (0, 6, 4), (0, 6, 6), (0, 4, 6), (0, 4, 4)))) cz_table = np.array(cz_table, dtype = int)