def test_crazy_linear_graph_builder():
""" Tests a 10-node crazy linear graph correctly built """
l, n = 5, 3
g = linear_graph(l)
cg = make_crazy(g, n)
cg_nodes, cg_edges = process_graph_nodes_edges(cg)
nodes = {(i, 0): [((i, 0), j) for j in range(n)] for i in range(l)}
edges = [((i, 0), (i + 1, 0)) for i in range(l - 1)]
edges = sorted(flatten([it.product(nodes[u], nodes[v])
for u, v in edges]))
nodes = sorted(flatten(nodes.values()))
assert cg_nodes == nodes
assert cg_edges == edges
def make_crazy(graph, n):
""" Converts a graph into it's crazily encoded version """
# Defines groupings of crazy nodes and edges between them
crazy_nodes = {node: [(node, i) for i in range(n)]
for node in graph.nodes()}
crazy_edges = flatten([it.product(crazy_nodes[u], crazy_nodes[v])
for u, v in graph.edges()])
# Creates graph and adds edges and nodes
crazy_graph = nx.Graph()
crazy_graph.add_nodes_from(flatten(crazy_nodes.values()))
crazy_graph.add_edges_from(crazy_edges)
# Assigns encoded attribute for to_GraphState
crazy_graph.encoded = True
return crazy_graph
def square_lattice(n, m, boundary=True):
""" Creates a square lattice with 2D coordinates """
mod_n = n + 1 if boundary else n
mod_m = m + 1 if boundary else m
g = nx.Graph()
nodes = list(it.product(range(n), range(m)))
edges = flatten([[((i, j), ((i + 1) % mod_n, j)),
((i, j), (i, (j + 1) % mod_m))] for i, j in nodes])
edges = [((u_x, u_y), (v_x, v_y)) for (u_x, u_y), (v_x, v_y) in edges
if max([u_x, v_x]) < n and max([u_y, v_y]) < m]
g.add_edges_from(edges)
return g
def make_ghz_like(graph, n):
""" Converts a graph into it's GHZ-encoded version """
# Defines groupings of GHZ-like nodes and edges between them
ghz_nodes = {node: [(node, i) for i in range(n)] for node in graph.nodes()}
ghz_edges = [((u, 0), (v, 0)) for u, v in graph.edges()] + \
[((node, 0), (node, i)) for node in graph.nodes() for i in range(1, n)]
# Creates graph and adds edges and nodes
ghz_graph = nx.Graph()
ghz_graph.add_nodes_from(flatten(ghz_nodes.values()))
ghz_graph.add_edges_from(ghz_edges)
# Assigns encoded attribute for to_GraphState
ghz_graph.encoded = True
return ghz_graph
def are_lc_equiv(g1, g2):
"""
Tests whether two graphs are equivalent up to local complementation.
If True, also returns every unitary such that |g2> = U|g1>.
"""
# Gets adjacency matrices and returns false if differing bases
am1, k1 = get_adjacency_matrix(g1)
am2, k2 = get_adjacency_matrix(g2)
dim1, dim2 = len(k1), len(k2)
if k1 != k2 or am1.shape != (dim1, dim1) or am2.shape != (dim2, dim2):
return False, None
# Defines binary matrices
Id = sp.eye(dim1)
S1 = sp.Matrix(am1).col_join(Id)
S2 = sp.Matrix(am2).col_join(Id)
# Defines symbolic variables
A = sp.symbols('a:' + str(dim1), bool=True)
B = sp.symbols('b:' + str(dim1), bool=True)
C = sp.symbols('c:' + str(dim1), bool=True)
D = sp.symbols('d:' + str(dim1), bool=True)
# Defines solution matrix basis
abcd = flatten(list(zip(A, B, C, D)))
no_vars = len(abcd)
no_qubits = no_vars // 4
# Creates symbolic binary matrix
A, B, C, D = sp.diag(*A), sp.diag(*B), sp.diag(*C), sp.diag(*D)
Q = A.row_join(B).col_join(C.row_join(D))
P = sp.zeros(dim1).row_join(Id).col_join(Id.row_join(sp.zeros(dim1)))
# Constructs matrix to solve
X = [i for i in S1.T * Q.T * P * S2]
X = np.array([[x.coeff(v) for v in abcd] for x in X], dtype=int)
# Removes any duplicated and all-zero rows
X = np.unique(X, axis=0)
X = X[~(X == 0).all(1)]
# Finds the solutions (the nullspace of X)
V = list(GF2nullspace(X))
if len(V) > 4:
V = [(v1 + v2) % 2 for v1, v2 in it.combinations(V, 2)]
else:
V = [sum(vs) % 2 for vs in powerset(V)]
V = [np.reshape(v, (no_qubits, 4)) for v in V]
V = [v for v in V if all((a * d + b * c) % 2 == 1 for a, b, c, d in v)]
if V:
V = [[bin2gate[tuple(r)] for r in v] for v in V]
return True, V
else:
return False, None
