Anders and Briegel in Python
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  1. """
  2. Provides an extremely basic graph structure, based on neighbour lists
  3. """
  4. from collections import defaultdict
  5. import itertools as it
  6. import tables as clifford
  7. class GraphState(object):
  8. def __init__(self):
  9. self.ngbh = defaultdict(set)
  10. self.vops = defaultdict(int)
  11. def add_edge(self, v1, v2):
  12. """ Add an edge between two vertices in the self """
  13. if not v1 in self.ngbh: self.vops[v1] = clifford.by_name["hadamard"]
  14. if not v2 in self.ngbh: self.vops[v2] = clifford.by_name["hadamard"]
  15. self.ngbh[v1].add(v2)
  16. self.ngbh[v2].add(v1)
  17. def del_edge(self, v1, v2):
  18. """ Delete an edge between two vertices in the self """
  19. self.ngbh[v1].remove(v2)
  20. self.ngbh[v2].remove(v1)
  21. def has_edge(self, v1, v2):
  22. """ Test existence of an edge between two vertices in the self """
  23. return v2 in self.ngbh[v1]
  24. def toggle_edge(self, v1, v2):
  25. """ Toggle an edge between two vertices in the self """
  26. if self.has_edge(v1, v2):
  27. self.del_edge(v1, v2)
  28. else:
  29. self.add_edge(v1, v2)
  30. def edgelist(self):
  31. """ Describe a graph as an edgelist """
  32. edges = frozenset(frozenset((i, n))
  33. for i, v in enumerate(self.ngbh.values())
  34. for n in v)
  35. return [tuple(e) for e in edges]
  36. def remove_vop(self, a, avoid):
  37. """ Reduces VOP[a] to the identity, avoiding (if possible) the use of vertex b as a swapping partner """
  38. others = self.ngbh[a] - {avoid}
  39. swap_qubit = others.pop() if others else avoid
  40. for v in reversed(clifford.decompositions[self.vops[a]]):
  41. self.local_complementation(a if v == "x" else swap_qubit)
  42. def cphase(self, a, b):
  43. """ Act a controlled-phase gate on two qubits """
  44. if self.ngbh[a] - {b}:
  45. self.remove_vop(a, b)
  46. if self.ngbh[b] - {a}:
  47. self.remove_vop(b, a)
  48. if self.ngbh[a] - {b}:
  49. self.remove_vop(a, b)
  50. edge = self.has_edge(a, b)
  51. new_edge, vops[a], vops[b] = cphase_table[edge, vops[a], vops[b]]
  52. if new_edge != edge:
  53. self.toggle_edge(a, b)
  54. def local_complementation(self, v):
  55. """ As defined in LISTING 1 of Anders & Briegel """
  56. for i, j in it.combinations(self.ngbh[v], 2):
  57. self.toggle_edge(i, j)
  58. # Update VOPs
  59. self.vops[v] = clifford.times_table[self.vops[v]][clifford.by_name["sqx"]]
  60. for i in self.ngbh[v]:
  61. self.vops[i] = clifford.times_table[self.vops[i]][clifford.by_name["msqz"]]