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 clifford
  7. def graph():
  8. """ Generate a graph with Hadamards on each qubit """
  9. #return defaultdict(set), defaultdict(lambda: clifford.by_name["hadamard"])
  10. return [set() for i in range(100)], [clifford.by_name["hadamard"] for i in range(100)]
  11. def add_edge(graph, v1, v2):
  12. """ Add an edge between two vertices in the graph """
  13. graph[v1].add(v2)
  14. graph[v2].add(v1)
  15. def del_edge(graph, v1, v2):
  16. """ Delete an edge between two vertices in the graph """
  17. graph[v1].remove(v2)
  18. graph[v2].remove(v1)
  19. def has_edge(graph, v1, v2):
  20. """ Test existence of an edge between two vertices in the graph """
  21. return v2 in graph[v1]
  22. def toggle_edge(graph, v1, v2):
  23. """ Toggle an edge between two vertices in the graph """
  24. if has_edge(graph, v1, v2):
  25. del_edge(graph, v1, v2)
  26. else:
  27. add_edge(graph, v1, v2)
  28. def edgelist(g):
  29. """ Describe a graph as an edgelist """
  30. edges = frozenset(frozenset((i, n))
  31. for i, v in enumerate(g)
  32. for n in v)
  33. return [tuple(e) for e in edges]
  34. def cphase(g, vops, a, b):
  35. """ Act a controlled-phase gate on two qubits """
  36. if g[a]-{b}: remove_vop(g, vops, a, b)
  37. if g[b]-{a}: remove_vop(g, vops, b, a)
  38. if g[a]-{b}: remove_vop(g, vops, a, b)
  39. edge = has_edge(g, a, b)
  40. new_edge, vops[a], vops[b] = cphase_table[edge, vops[a], vops[b]]
  41. if new_edge != edge:
  42. toggle_edge(g, a, b)
  43. def remove_vop(g, vops, a, avoid):
  44. """ Reduces VOP[a] to the identity, avoiding (if possible) the use of vertex b as a swapping partner """
  45. others = g[a] - {avoid}
  46. swap_qubit = others.pop() if others else avoid
  47. for v in reversed(clifford.decompositions[vops[a]]):
  48. local_complementation(g, vops, a if v == "x" else swap_qubit)
  49. def local_complementation(g, vops, v):
  50. """ As defined in LISTING 1 of Anders & Briegel """
  51. for i, j in it.combinations(g[v], 2):
  52. toggle_edge(g, i, j)
  53. # Update VOPs
  54. vops[v] = clifford.times_table[vops[v]][clifford.by_name["sqx"]]
  55. for i in g[v]:
  56. vops[i] = clifford.times_table[vops[i]][clifford.by_name["msqz"]]