Anders and Briegel in Python
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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)