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Anders and Briegel in Python
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abp/abp/anders_cz.py

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  1. """

  2. Copied from Anders' original C++ implementation

  3. S. Anders, H. J. Briegel: Fast Simulation of Stabilizer Circuits using a Graph State Formalism quant-ph/0504117

  4. """

  5. import numpy as np

  6. cz_table = ((((1, 0, 0), (1, 0, 0), (1, 0, 3), (1, 0, 3), (1, 0, 5), (1, 0, 5), 

  7.    (1, 0, 6), (1, 0, 6), (0, 3, 8), (0, 3, 8), (0, 0, 10), (0, 0, 10), 

  8.    (1, 0, 3), (1, 0, 3), (1, 0, 0), (1, 0, 0), (1, 0, 6), (1, 0, 6), 

  9.    (1, 0, 5), (1, 0, 5), (0, 0, 10), (0, 0, 10), (0, 3, 8), (0, 3, 8)), 

  10.   ((1, 0, 0), (1, 0, 0), (1, 0, 3), (1, 0, 3), (1, 0, 5), (1, 0, 5), 

  11.    (1, 0, 6), (1, 0, 6), (0, 2, 8), (0, 2, 8), (0, 0, 10), (0, 0, 10), 

  12.    (1, 0, 3), (1, 0, 3), (1, 0, 0), (1, 0, 0), (1, 0, 6), (1, 0, 6), 

  13.    (1, 0, 5), (1, 0, 5), (0, 0, 10), (0, 0, 10), (0, 2, 8), (0, 2, 8)), 

  14.   ((1, 2, 3), (1, 0, 1), (1, 0, 2), (1, 2, 0), (1, 0, 4), (1, 2, 6), 

  15.    (1, 2, 5), (1, 0, 7), (0, 0, 8), (0, 0, 8), (0, 2, 10), (0, 2, 10), 

  16.    (1, 0, 2), (1, 0, 2), (1, 0, 1), (1, 0, 1), (1, 0, 7), (1, 0, 7), 

  17.    (1, 0, 4), (1, 0, 4), (0, 2, 10), (0, 2, 10), (0, 0, 8), (0, 0, 8)), 

  18.   ((1, 3, 0), (1, 0, 1), (1, 0, 2), (1, 3, 3), (1, 0, 4), (1, 3, 5), 

  19.    (1, 3, 6), (1, 0, 7), (0, 0, 8), (0, 0, 8), (0, 3, 10), (0, 3, 10), 

  20.    (1, 0, 2), (1, 0, 2), (1, 0, 1), (1, 0, 1), (1, 0, 7), (1, 0, 7), 

  21.    (1, 0, 4), (1, 0, 4), (0, 3, 10), (0, 3, 10), (0, 0, 8), (0, 0, 8)), 

  22.   ((1, 4, 3), (1, 4, 3), (1, 4, 0), (1, 4, 0), (1, 4, 6), (1, 4, 6), 

  23.    (1, 4, 5), (1, 4, 5), (0, 6, 8), (0, 6, 8), (0, 4, 10), (0, 4, 10), 

  24.    (1, 4, 0), (1, 4, 0), (1, 4, 3), (1, 4, 3), (1, 4, 5), (1, 4, 5), 

  25.    (1, 4, 6), (1, 4, 6), (0, 4, 10), (0, 4, 10), (0, 6, 8), (0, 6, 8)), 

  26.   ((1, 5, 0), (1, 5, 0), (1, 5, 3), (1, 5, 3), (1, 5, 5), (1, 5, 5), 

  27.    (1, 5, 6), (1, 5, 6), (0, 6, 8), (0, 6, 8), (0, 5, 10), (0, 5, 10), 

  28.    (1, 5, 3), (1, 5, 3), (1, 5, 0), (1, 5, 0), (1, 5, 6), (1, 5, 6), 

  29.    (1, 5, 5), (1, 5, 5), (0, 5, 10), (0, 5, 10), (0, 6, 8), (0, 6, 8)), 

  30.   ((1, 6, 0), (1, 5, 1), (1, 5, 2), (1, 6, 3), (1, 5, 4), (1, 6, 5), 

  31.    (1, 6, 6), (1, 5, 7), (0, 5, 8), (0, 5, 8), (0, 6, 10), (0, 6, 10), 

  32.    (1, 5, 2), (1, 5, 2), (1, 5, 1), (1, 5, 1), (1, 5, 7), (1, 5, 7), 

  33.    (1, 5, 4), (1, 5, 4), (0, 6, 10), (0, 6, 10), (0, 5, 8), (0, 5, 8)), 

  34.   ((1, 6, 0), (1, 4, 2), (1, 4, 1), (1, 6, 3), (1, 4, 7), (1, 6, 5), 

  35.    (1, 6, 6), (1, 4, 4), (0, 4, 8), (0, 4, 8), (0, 6, 10), (0, 6, 10), 

  36.    (1, 4, 1), (1, 4, 1), (1, 4, 2), (1, 4, 2), (1, 4, 4), (1, 4, 4), 

  37.    (1, 4, 7), (1, 4, 7), (0, 6, 10), (0, 6, 10), (0, 4, 8), (0, 4, 8)), 

  38.   ((0, 8, 3), (0, 8, 2), (0, 8, 0), (0, 8, 0), (0, 8, 6), (0, 8, 6), 

  39.    (0, 8, 5), (0, 8, 4), (0, 8, 8), (0, 8, 8), (0, 8, 10), (0, 8, 10), 

  40.    (0, 8, 0), (0, 8, 0), (0, 8, 2), (0, 8, 2), (0, 8, 4), (0, 8, 4), 

  41.    (0, 8, 6), (0, 8, 6), (0, 8, 10), (0, 8, 10), (0, 8, 8), (0, 8, 8)), 

  42.   ((0, 8, 3), (0, 8, 2), (0, 8, 0), (0, 8, 0), (0, 8, 6), (0, 8, 6), 

  43.    (0, 8, 5), (0, 8, 4), (0, 8, 8), (0, 8, 8), (0, 8, 10), (0, 8, 10), 

  44.    (0, 8, 0), (0, 8, 0), (0, 8, 2), (0, 8, 2), (0, 8, 4), (0, 8, 4), 

  45.    (0, 8, 6), (0, 8, 6), (0, 8, 10), (0, 8, 10), (0, 8, 8), (0, 8, 8)), 

  46.   ((0, 10, 0), (0, 10, 0), (0, 10, 2), (0, 10, 3), (0, 10, 4), (0, 10, 5), 

  47.    (0, 10, 6), (0, 10, 6), (0, 10, 8), (0, 10, 8), (0, 10, 10), (0, 10, 10), 

  48.    (0, 10, 2), (0, 10, 2), (0, 10, 0), (0, 10, 0), (0, 10, 6), (0, 10, 6), 

  49.    (0, 10, 4), (0, 10, 4), (0, 10, 10), (0, 10, 10), (0, 10, 8), (0, 10, 8)), 

  50.   ((0, 10, 0), (0, 10, 0), (0, 10, 2), (0, 10, 3), (0, 10, 4), (0, 10, 5), 

  51.    (0, 10, 6), (0, 10, 6), (0, 10, 8), (0, 10, 8), (0, 10, 10), (0, 10, 10), 

  52.    (0, 10, 2), (0, 10, 2), (0, 10, 0), (0, 10, 0), (0, 10, 6), (0, 10, 6), 

  53.    (0, 10, 4), (0, 10, 4), (0, 10, 10), (0, 10, 10), (0, 10, 8), (0, 10, 8)), 

  54.   ((1, 2, 3), (1, 0, 1), (1, 0, 2), (1, 2, 0), (1, 0, 4), (1, 2, 6), 

  55.    (1, 2, 5), (1, 0, 7), (0, 0, 8), (0, 0, 8), (0, 2, 10), (0, 2, 10), 

  56.    (1, 0, 2), (1, 0, 2), (1, 0, 1), (1, 0, 1), (1, 0, 7), (1, 0, 7), 

  57.    (1, 0, 4), (1, 0, 4), (0, 2, 10), (0, 2, 10), (0, 0, 8), (0, 0, 8)), 

  58.   ((1, 2, 3), (1, 0, 1), (1, 0, 2), (1, 2, 0), (1, 0, 4), (1, 2, 6), 

  59.    (1, 2, 5), (1, 0, 7), (0, 0, 8), (0, 0, 8), (0, 2, 10), (0, 2, 10), 

  60.    (1, 0, 2), (1, 0, 2), (1, 0, 1), (1, 0, 1), (1, 0, 7), (1, 0, 7), 

  61.    (1, 0, 4), (1, 0, 4), (0, 2, 10), (0, 2, 10), (0, 0, 8), (0, 0, 8)), 

  62.   ((1, 0, 0), (1, 0, 0), (1, 0, 3), (1, 0, 3), (1, 0, 5), (1, 0, 5), 

  63.    (1, 0, 6), (1, 0, 6), (0, 2, 8), (0, 2, 8), (0, 0, 10), (0, 0, 10), 

  64.    (1, 0, 3), (1, 0, 3), (1, 0, 0), (1, 0, 0), (1, 0, 6), (1, 0, 6), 

  65.    (1, 0, 5), (1, 0, 5), (0, 0, 10), (0, 0, 10), (0, 2, 8), (0, 2, 8)), 

  66.   ((1, 0, 0), (1, 0, 0), (1, 0, 3), (1, 0, 3), (1, 0, 5), (1, 0, 5), 

  67.    (1, 0, 6), (1, 0, 6), (0, 2, 8), (0, 2, 8), (0, 0, 10), (0, 0, 10), 

  68.    (1, 0, 3), (1, 0, 3), (1, 0, 0), (1, 0, 0), (1, 0, 6), (1, 0, 6), 

  69.    (1, 0, 5), (1, 0, 5), (0, 0, 10), (0, 0, 10), (0, 2, 8), (0, 2, 8)), 

  70.   ((1, 6, 0), (1, 4, 2), (1, 4, 1), (1, 6, 3), (1, 4, 7), (1, 6, 5), 

  71.    (1, 6, 6), (1, 4, 4), (0, 4, 8), (0, 4, 8), (0, 6, 10), (0, 6, 10), 

  72.    (1, 4, 1), (1, 4, 1), (1, 4, 2), (1, 4, 2), (1, 4, 4), (1, 4, 4), 

  73.    (1, 4, 7), (1, 4, 7), (0, 6, 10), (0, 6, 10), (0, 4, 8), (0, 4, 8)), 

  74.   ((1, 6, 0), (1, 4, 2), (1, 4, 1), (1, 6, 3), (1, 4, 7), (1, 6, 5), 

  75.    (1, 6, 6), (1, 4, 4), (0, 4, 8), (0, 4, 8), (0, 6, 10), (0, 6, 10), 

  76.    (1, 4, 1), (1, 4, 1), (1, 4, 2), (1, 4, 2), (1, 4, 4), (1, 4, 4), 

  77.    (1, 4, 7), (1, 4, 7), (0, 6, 10), (0, 6, 10), (0, 4, 8), (0, 4, 8)), 

  78.   ((1, 4, 3), (1, 4, 3), (1, 4, 0), (1, 4, 0), (1, 4, 6), (1, 4, 6), 

  79.    (1, 4, 5), (1, 4, 5), (0, 6, 8), (0, 6, 8), (0, 4, 10), (0, 4, 10), 

  80.    (1, 4, 0), (1, 4, 0), (1, 4, 3), (1, 4, 3), (1, 4, 5), (1, 4, 5), 

  81.    (1, 4, 6), (1, 4, 6), (0, 4, 10), (0, 4, 10), (0, 6, 8), (0, 6, 8)), 

  82.   ((1, 4, 3), (1, 4, 3), (1, 4, 0), (1, 4, 0), (1, 4, 6), (1, 4, 6), 

  83.    (1, 4, 5), (1, 4, 5), (0, 6, 8), (0, 6, 8), (0, 4, 10), (0, 4, 10), 

  84.    (1, 4, 0), (1, 4, 0), (1, 4, 3), (1, 4, 3), (1, 4, 5), (1, 4, 5), 

  85.    (1, 4, 6), (1, 4, 6), (0, 4, 10), (0, 4, 10), (0, 6, 8), (0, 6, 8)), 

  86.   ((0, 10, 0), (0, 10, 0), (0, 10, 2), (0, 10, 3), (0, 10, 4), (0, 10, 5), 

  87.    (0, 10, 6), (0, 10, 6), (0, 10, 8), (0, 10, 8), (0, 10, 10), (0, 10, 10), 

  88.    (0, 10, 2), (0, 10, 2), (0, 10, 0), (0, 10, 0), (0, 10, 6), (0, 10, 6), 

  89.    (0, 10, 4), (0, 10, 4), (0, 10, 10), (0, 10, 10), (0, 10, 8), (0, 10, 8)), 

  90.   ((0, 10, 0), (0, 10, 0), (0, 10, 2), (0, 10, 3), (0, 10, 4), (0, 10, 5), 

  91.    (0, 10, 6), (0, 10, 6), (0, 10, 8), (0, 10, 8), (0, 10, 10), (0, 10, 10), 

  92.    (0, 10, 2), (0, 10, 2), (0, 10, 0), (0, 10, 0), (0, 10, 6), (0, 10, 6), 

  93.    (0, 10, 4), (0, 10, 4), (0, 10, 10), (0, 10, 10), (0, 10, 8), (0, 10, 8)), 

  94.   ((0, 8, 3), (0, 8, 2), (0, 8, 0), (0, 8, 0), (0, 8, 6), (0, 8, 6), 

  95.    (0, 8, 5), (0, 8, 4), (0, 8, 8), (0, 8, 8), (0, 8, 10), (0, 8, 10), 

  96.    (0, 8, 0), (0, 8, 0), (0, 8, 2), (0, 8, 2), (0, 8, 4), (0, 8, 4), 

  97.    (0, 8, 6), (0, 8, 6), (0, 8, 10), (0, 8, 10), (0, 8, 8), (0, 8, 8)), 

  98.   ((0, 8, 3), (0, 8, 2), (0, 8, 0), (0, 8, 0), (0, 8, 6), (0, 8, 6), 

  99.    (0, 8, 5), (0, 8, 4), (0, 8, 8), (0, 8, 8), (0, 8, 10), (0, 8, 10), 

  100.    (0, 8, 0), (0, 8, 0), (0, 8, 2), (0, 8, 2), (0, 8, 4), (0, 8, 4), 

  101.    (0, 8, 6), (0, 8, 6), (0, 8, 10), (0, 8, 10), (0, 8, 8), (0, 8, 8))), 

  102.  (((0, 0, 0), (0, 3, 0), (0, 3, 2), (0, 0, 3), (0, 3, 4), (0, 0, 5), 

  103.    (0, 0, 6), (0, 3, 6), (1, 5, 23), (1, 5, 22), (1, 5, 21), (1, 5, 20), 

  104.    (0, 5, 2), (0, 6, 2), (0, 5, 0), (0, 6, 0), (0, 6, 6), (0, 5, 6), 

  105.    (0, 6, 4), (0, 5, 4), (1, 5, 10), (1, 5, 11), (1, 5, 8), (1, 5, 9)), 

  106.   ((0, 0, 3), (0, 2, 2), (0, 2, 0), (0, 0, 0), (0, 2, 6), (0, 0, 6), 

  107.    (0, 0, 5), (0, 2, 4), (1, 4, 23), (1, 4, 22), (1, 4, 21), (1, 4, 20), 

  108.    (0, 6, 0), (0, 4, 0), (0, 6, 2), (0, 4, 2), (0, 4, 4), (0, 6, 4), 

  109.    (0, 4, 6), (0, 6, 6), (1, 4, 10), (1, 4, 11), (1, 4, 8), (1, 4, 9)), 

  110.   ((0, 2, 3), (0, 0, 2), (0, 0, 0), (0, 2, 0), (0, 0, 6), (0, 2, 6), 

  111.    (0, 2, 5), (0, 0, 4), (1, 4, 22), (1, 4, 23), (1, 4, 20), (1, 4, 21), 

  112.    (0, 4, 0), (0, 6, 0), (0, 4, 2), (0, 6, 2), (0, 6, 4), (0, 4, 4), 

  113.    (0, 6, 6), (0, 4, 6), (1, 4, 11), (1, 4, 10), (1, 4, 9), (1, 4, 8)), 

  114.   ((0, 3, 0), (0, 0, 0), (0, 0, 2), (0, 3, 3), (0, 0, 4), (0, 3, 5), 

  115.    (0, 3, 6), (0, 0, 6), (1, 5, 22), (1, 5, 23), (1, 5, 20), (1, 5, 21), 

  116.    (0, 6, 2), (0, 5, 2), (0, 6, 0), (0, 5, 0), (0, 5, 6), (0, 6, 6), 

  117.    (0, 5, 4), (0, 6, 4), (1, 5, 11), (1, 5, 10), (1, 5, 9), (1, 5, 8)), 

  118.   ((0, 4, 3), (0, 6, 2), (0, 6, 0), (0, 4, 0), (0, 6, 6), (0, 4, 6), 

  119.    (0, 4, 5), (0, 6, 4), (1, 0, 21), (1, 0, 20), (1, 0, 23), (1, 0, 22), 

  120.    (0, 0, 0), (0, 2, 0), (0, 0, 2), (0, 2, 2), (0, 2, 4), (0, 0, 4), 

  121.    (0, 2, 6), (0, 0, 6), (1, 0, 8), (1, 0, 9), (1, 0, 10), (1, 0, 11)), 

  122.   ((0, 5, 0), (0, 6, 0), (0, 6, 2), (0, 5, 3), (0, 6, 4), (0, 5, 5), 

  123.    (0, 5, 6), (0, 6, 6), (1, 0, 22), (1, 0, 23), (1, 0, 20), (1, 0, 21), 

  124.    (0, 3, 2), (0, 0, 2), (0, 3, 0), (0, 0, 0), (0, 0, 6), (0, 3, 6), 

  125.    (0, 0, 4), (0, 3, 4), (1, 0, 11), (1, 0, 10), (1, 0, 9), (1, 0, 8)), 

  126.   ((0, 6, 0), (0, 5, 0), (0, 5, 2), (0, 6, 3), (0, 5, 4), (0, 6, 5), 

  127.    (0, 6, 6), (0, 5, 6), (1, 0, 23), (1, 0, 22), (1, 0, 21), (1, 0, 20), 

  128.    (0, 0, 2), (0, 3, 2), (0, 0, 0), (0, 3, 0), (0, 3, 6), (0, 0, 6), 

  129.    (0, 3, 4), (0, 0, 4), (1, 0, 10), (1, 0, 11), (1, 0, 8), (1, 0, 9)), 

  130.   ((0, 6, 3), (0, 4, 2), (0, 4, 0), (0, 6, 0), (0, 4, 6), (0, 6, 6), 

  131.    (0, 6, 5), (0, 4, 4), (1, 0, 20), (1, 0, 21), (1, 0, 22), (1, 0, 23), 

  132.    (0, 2, 0), (0, 0, 0), (0, 2, 2), (0, 0, 2), (0, 0, 4), (0, 2, 4), 

  133.    (0, 0, 6), (0, 2, 6), (1, 0, 9), (1, 0, 8), (1, 0, 11), (1, 0, 10)), 

  134.   ((1, 22, 6), (1, 20, 5), (1, 20, 6), (1, 22, 5), (1, 20, 3), (1, 22, 0), 

  135.    (1, 22, 3), (1, 20, 0), (0, 0, 0), (0, 0, 2), (0, 2, 2), (0, 2, 0), 

  136.    (0, 6, 6), (0, 4, 4), (0, 6, 4), (0, 4, 6), (0, 4, 2), (0, 6, 0), 

  137.    (0, 4, 0), (0, 6, 2), (0, 2, 4), (0, 2, 6), (0, 0, 6), (0, 0, 4)), 

  138.   ((1, 22, 5), (1, 20, 6), (1, 20, 5), (1, 22, 6), (1, 20, 0), (1, 22, 3), 

  139.    (1, 22, 0), (1, 20, 3), (0, 2, 0), (0, 2, 2), (0, 0, 2), (0, 0, 0), 

  140.    (0, 4, 6), (0, 6, 4), (0, 4, 4), (0, 6, 6), (0, 6, 2), (0, 4, 0), 

  141.    (0, 6, 0), (0, 4, 2), (0, 0, 4), (0, 0, 6), (0, 2, 6), (0, 2, 4)), 

  142.   ((1, 20, 6), (1, 20, 7), (1, 20, 4), (1, 20, 5), (1, 20, 1), (1, 20, 0), 

  143.    (1, 20, 3), (1, 20, 2), (0, 2, 2), (0, 2, 0), (0, 0, 0), (0, 0, 2), 

  144.    (0, 6, 4), (0, 4, 6), (0, 6, 6), (0, 4, 4), (0, 4, 0), (0, 6, 2), 

  145.    (0, 4, 2), (0, 6, 0), (0, 0, 6), (0, 0, 4), (0, 2, 4), (0, 2, 6)), 

  146.   ((1, 20, 5), (1, 20, 4), (1, 20, 7), (1, 20, 6), (1, 20, 2), (1, 20, 3), 

  147.    (1, 20, 0), (1, 20, 1), (0, 0, 2), (0, 0, 0), (0, 2, 0), (0, 2, 2), 

  148.    (0, 4, 4), (0, 6, 6), (0, 4, 6), (0, 6, 4), (0, 6, 0), (0, 4, 2), 

  149.    (0, 6, 2), (0, 4, 0), (0, 2, 6), (0, 2, 4), (0, 0, 4), (0, 0, 6)), 

  150.   ((0, 2, 5), (0, 0, 6), (0, 0, 4), (0, 2, 6), (0, 0, 0), (0, 2, 3), 

  151.    (0, 2, 0), (0, 0, 2), (0, 6, 6), (0, 6, 4), (0, 4, 6), (0, 4, 4), 

  152.    (1, 16, 18), (1, 16, 19), (1, 16, 16), (1, 16, 17), (1, 16, 12), 

  153.    (1, 16, 13), (1, 16, 14), (1, 16, 15), (0, 4, 2), (0, 4, 0), (0, 6, 2), 

  154.    (0, 6, 0)), ((0, 2, 6), (0, 0, 4), (0, 0, 6), (0, 2, 5), (0, 0, 2), 

  155.    (0, 2, 0), (0, 2, 3), (0, 0, 0), (0, 4, 4), (0, 4, 6), (0, 6, 4), 

  156.    (0, 6, 6), (1, 16, 17), (1, 16, 16), (1, 16, 19), (1, 16, 18), 

  157.    (1, 16, 15), (1, 16, 14), (1, 16, 13), (1, 16, 12), (0, 6, 0), (0, 6, 2), 

  158.    (0, 4, 0), (0, 4, 2)), ((0, 0, 5), (0, 2, 6), (0, 2, 4), (0, 0, 6), 

  159.    (0, 2, 0), (0, 0, 3), (0, 0, 0), (0, 2, 2), (0, 4, 6), (0, 4, 4), 

  160.    (0, 6, 6), (0, 6, 4), (1, 16, 16), (1, 16, 17), (1, 16, 18), (1, 16, 19), 

  161.    (1, 16, 14), (1, 16, 15), (1, 16, 12), (1, 16, 13), (0, 6, 2), (0, 6, 0), 

  162.    (0, 4, 2), (0, 4, 0)), ((0, 0, 6), (0, 2, 4), (0, 2, 6), (0, 0, 5), 

  163.    (0, 2, 2), (0, 0, 0), (0, 0, 3), (0, 2, 0), (0, 6, 4), (0, 6, 6), 

  164.    (0, 4, 4), (0, 4, 6), (1, 16, 19), (1, 16, 18), (1, 16, 17), (1, 16, 16), 

  165.    (1, 16, 13), (1, 16, 12), (1, 16, 15), (1, 16, 14), (0, 4, 0), (0, 4, 2), 

  166.    (0, 6, 0), (0, 6, 2)), ((0, 6, 6), (0, 4, 4), (0, 4, 6), (0, 6, 5), 

  167.    (0, 4, 2), (0, 6, 0), (0, 6, 3), (0, 4, 0), (0, 2, 4), (0, 2, 6), 

  168.    (0, 0, 4), (0, 0, 6), (1, 12, 16), (1, 12, 17), (1, 12, 18), (1, 12, 19), 

  169.    (1, 12, 14), (1, 12, 15), (1, 12, 12), (1, 12, 13), (0, 0, 0), (0, 0, 2), 

  170.    (0, 2, 0), (0, 2, 2)), ((0, 6, 5), (0, 4, 6), (0, 4, 4), (0, 6, 6), 

  171.    (0, 4, 0), (0, 6, 3), (0, 6, 0), (0, 4, 2), (0, 0, 6), (0, 0, 4), 

  172.    (0, 2, 6), (0, 2, 4), (1, 12, 19), (1, 12, 18), (1, 12, 17), (1, 12, 16), 

  173.    (1, 12, 13), (1, 12, 12), (1, 12, 15), (1, 12, 14), (0, 2, 2), (0, 2, 0), 

  174.    (0, 0, 2), (0, 0, 0)), ((0, 4, 6), (0, 6, 4), (0, 6, 6), (0, 4, 5), 

  175.    (0, 6, 2), (0, 4, 0), (0, 4, 3), (0, 6, 0), (0, 0, 4), (0, 0, 6), 

  176.    (0, 2, 4), (0, 2, 6), (1, 12, 18), (1, 12, 19), (1, 12, 16), (1, 12, 17), 

  177.    (1, 12, 12), (1, 12, 13), (1, 12, 14), (1, 12, 15), (0, 2, 0), (0, 2, 2), 

  178.    (0, 0, 0), (0, 0, 2)), ((0, 4, 5), (0, 6, 6), (0, 6, 4), (0, 4, 6), 

  179.    (0, 6, 0), (0, 4, 3), (0, 4, 0), (0, 6, 2), (0, 2, 6), (0, 2, 4), 

  180.    (0, 0, 6), (0, 0, 4), (1, 12, 17), (1, 12, 16), (1, 12, 19), (1, 12, 18), 

  181.    (1, 12, 15), (1, 12, 14), (1, 12, 13), (1, 12, 12), (0, 0, 2), (0, 0, 0), 

  182.    (0, 2, 2), (0, 2, 0)), ((1, 10, 5), (1, 8, 6), (1, 8, 5), (1, 10, 6), 

  183.    (1, 8, 0), (1, 10, 3), (1, 10, 0), (1, 8, 3), (0, 4, 2), (0, 4, 0), 

  184.    (0, 6, 0), (0, 6, 2), (0, 2, 4), (0, 0, 6), (0, 2, 6), (0, 0, 4), 

  185.    (0, 0, 0), (0, 2, 2), (0, 0, 2), (0, 2, 0), (0, 6, 6), (0, 6, 4), 

  186.    (0, 4, 4), (0, 4, 6)), ((1, 10, 6), (1, 8, 5), (1, 8, 6), (1, 10, 5), 

  187.    (1, 8, 3), (1, 10, 0), (1, 10, 3), (1, 8, 0), (0, 6, 2), (0, 6, 0), 

  188.    (0, 4, 0), (0, 4, 2), (0, 0, 4), (0, 2, 6), (0, 0, 6), (0, 2, 4), 

  189.    (0, 2, 0), (0, 0, 2), (0, 2, 2), (0, 0, 0), (0, 4, 6), (0, 4, 4), 

  190.    (0, 6, 4), (0, 6, 6)), ((1, 8, 5), (1, 8, 4), (1, 8, 7), (1, 8, 6), 

  191.    (1, 8, 2), (1, 8, 3), (1, 8, 0), (1, 8, 1), (0, 6, 0), (0, 6, 2), 

  192.    (0, 4, 2), (0, 4, 0), (0, 2, 6), (0, 0, 4), (0, 2, 4), (0, 0, 6), 

  193.    (0, 0, 2), (0, 2, 0), (0, 0, 0), (0, 2, 2), (0, 4, 4), (0, 4, 6), 

  194.    (0, 6, 6), (0, 6, 4)), ((1, 8, 6), (1, 8, 7), (1, 8, 4), (1, 8, 5), 

  195.    (1, 8, 1), (1, 8, 0), (1, 8, 3), (1, 8, 2), (0, 4, 0), (0, 4, 2), 

  196.    (0, 6, 2), (0, 6, 0), (0, 0, 6), (0, 2, 4), (0, 0, 4), (0, 2, 6), 

  197.    (0, 2, 2), (0, 0, 0), (0, 2, 0), (0, 0, 2), (0, 6, 4), (0, 6, 6), 

  198.    (0, 4, 6), (0, 4, 4))))

  199. cz_table = np.array(cz_table, dtype = int)