def succprob_poly_withMC(graph, transm=0.9, MC_samples=1000, t_sampl_func=None, in_qubit=0, printing=False):
"""
Returns an analytical estimate (lower bound) of the success probability for recovering a qubit encoded in the
graph, in the form of a polinomial of the form
a_1 t^(e_11) (1-t)^(e_12) + a_2 t^(e_21) (1-t)^(e_22) + ... + a_n t^(e_n1) (1-t)^(e_n2)
returning it in the form of the dictionary {(e_11, e_12): a_1, (e_21, e_22): a_2, ... , (e_n1, e_n2): a_n}
"""
gstate = GraphState(graph)
poss_stabs_list = get_possible_stabs_meas(gstate, in_qubit)
if t_sampl_func == None:
trans_sampl_func = lambda t: transm
else:
trans_sampl_func = lambda t: t_sampl_func(t)
success_measurements = []
for test_ix in range(MC_samples):
# print(trans_sampl_func(transm))
decoding_succ, decoding_meas = MC_decoding(poss_stabs_list, trans_sampl_func(transm),
in_qubit, printing=False, provide_measures=True)
if decoding_succ:
success_measurements.append(decoding_meas)
## filter out duplicates
# print('success_measurements', success_measurements)
success_meas_filter = list(set(success_measurements))
polynom_all_exponents = [(len(this_meas[0]), len(this_meas[1])) for this_meas in success_meas_filter]
if printing:
print("success_meas_filter :", success_meas_filter)
print("polynom_all_exponents :", polynom_all_exponents)
return dict(Counter(polynom_all_exponents))
def graphstate_from_nodes_and_edges(graph_nodes, graph_edges):
graph = nx.Graph()
graph.add_nodes_from(graph_nodes)
graph.add_edges_from(graph_edges)
return GraphState(graph)
##############################
### MAIN ###
##############################
if __name__ == '__main__':
import matplotlib.pyplot as plt
## index of the input qubit (output qubit is free)
in_qubit = 0
## define graph state
# three graph
branching = [2, 1]
graph = gen_tree_graph(branching)
gstate = GraphState(graph)
### fully connected graph
# graph = gen_fullyconnected_graph(7)
# gstate = GraphState(graph)
## get list of possible measurements to encode & decode the state
poss_stabs_list = get_possible_stabs_meas(gstate, in_qubit)
##############################################################################
################################### SINGLE TEST ##############################
##############################################################################
## define channel transmission
transmission = 0.7
decoding_succ = MC_decoding(poss_stabs_list,
else:
return np.real(real_roots[0])
if __name__ == '__main__':
import matplotlib.pyplot as plt
in_qubit = 0
### random graph
# graph = gen_random_connected_graph(6)
# gstate = GraphState(graph)
### ring graph
graph = gen_ring_graph(5)
gstate = GraphState(graph)
### 5-qubit Shor-code graph
# graph = nx.Graph()
# nodes = list(range(6))
# graph.add_nodes_from(nodes)
# graph.add_edges_from(product([0], nodes[1:]))
# graph.add_edges_from([(nodes[i], nodes[i + 1]) for i in range(1, 5)] + [(5, 1)])
# gstate = GraphState(graph)
### Cascaded 3-rings
# graph = nx.Graph()
# nodes = list(range(7))
# graph.add_nodes_from(nodes)
# graph.add_edges_from([(0, 2), (0, 1), (1, 2), (1, 6), (1, 5), (5, 6), (2, 3), (2, 4), (3, 4)])
# gstate = GraphState(graph)
import qecc as q
# stab_gens = ["XZII", "ZXZI", "IZXZ", "IIZX"]
# stab_gens = ["ZZII", "XXZI", "IZXZ", "IIZX"] ##H on first
# stab_gens = ["ZXII", "XZZI", "IXXZ", "IIZX"] ##H on first and second
# stab_gens = ["ZZXXX", "XXXXX", "XZZXX", "XXZZX", "XXXZZ"] # GHZ
stab_gens = ["XZZXI", "IXZZX", "XIXZZ", "ZXIXZ", "ZZZZZ"] ## 5-qubit code
# stab_gens = ["ZZIIIIIII", "ZIZIIIIII", "IIIZZIIII", "IIIZIZIII", "IIIIIIZZI", "IIIIIIZIZ",
# "XXXXXXIII", "XXXIIIXXX", "ZIIIZIZII"] ## Shor code
gen_list = q.PauliList(stab_gens)
stab_state = StabState(gen_list)
graph_equiv, adj_mat, clifford_transf, basis_change_mat = stab_to_graph(
stab_state)
graph_state = GraphState(graph_equiv)
print('Adjacency matrix of equivalent graph state:')
print(adj_mat)
print('Local Clifford transformation:')
print(clifford_transf)
# SOME TARGET GRAPHS
######## 4 qubit line
# graph_targ = nx.Graph()
# graph_targ.add_nodes_from([0, 1, 2, 3])
# graph_targ.add_edges_from([(0, 1), (1, 2), (2, 3)])
######## graph for 5-qubit star
# graph_targ = nx.Graph()
global_phase = np.pi / 7
### add Z rotation on first qubit
theta = np.pi / 5
added_U = np.kron(np.array([[1, 0], [0, np.exp(1.j * theta)]]),
np.identity(2**(qubits_num - 1)))
### print stuff?
print_tests = False
for edges_conf_ix, graph_edges in enumerate(all_graphs_by_edges):
# print('Testing graph', edges_conf_ix, 'of', num_graphs)
graph = nx.Graph()
graph.add_nodes_from(graph_nodes)
graph.add_edges_from(graph_edges)
this_gstate = GraphState(graph)
target_adjmat = this_gstate.adj_mat()
vect_state0 = this_gstate.graph_vecstate()
vect_state = added_U @ vect_state0
vect_state = np.exp(1.j * global_phase) * vect_state
test_if_graph, Amat, _ = vector_is_graphstate(vect_state,
print_error=False)
if print_tests:
print()
print('target_adjmat:')
print(target_adjmat)
print('vect_state0')
print(vect_state0)
def graphstate_from_nodes_and_edges(graph_nodes, graph_edges):
return GraphState(graph_from_nodes_and_edges(graph_nodes, graph_edges))
full_new_lc_class = lc_equivalence_class(
graph, fixed_node=input_qubit)
obt_graphs = obt_graphs + full_new_lc_class
used_rots = used_rots + [
rots_list for i in range(len(full_new_lc_class))
]
# print('Total class representatives number:', len(lc_class_representatives))
# print('Total graph number:', len(obt_graphs))
else:
if not arreq_in_list(adj_mat, obt_graphs):
# print("Got a NEW graph! Rotation sequence:", rots_list, " Local Z phases:", local_phases, " Applied hadamards: ", applied_hadamard)
print(rots_list, local_phases, applied_hadamard)
obt_graphs.append(adj_mat)
used_rots.append(rots_list)
plt.subplot()
gstate = GraphState(nx.from_numpy_matrix(adj_mat))
gstate.image(with_labels=True)
plt.show()
if not include_lc:
obt_graphs = [nx.from_numpy_matrix(this_A) for this_A in obt_graphs]
# plot all obtained graphs
num_graphs = len(obt_graphs)
n = int(np.sqrt(num_graphs))
n_plot_rows = n
n_plot_cols = num_graphs / n
if not isinstance(n_plot_cols, int):
n_plot_cols = int(n_plot_cols) + 1
# for code_ix in range(num_graphs):