def P2_update_coefficients(num_nodes, dim, graph_type, cmat_in):
dim_list = list(range(0, dim))
numA, numB = assign_nodes(num_nodes, graph_type)
normK = 0
for x in range(0, dim**numB):
for y in range(0, dim**numA):
for z in range(0, y):
normK += cmat_in[y, x] * cmat_in[z, x] + cmat_in[
z, x] * cmat_in[y, x]
normK += (cmat_in[y, x])**2
indices = list(product(dim_list, repeat=numA)) #all labels
coef_mat = np.zeros((dim**numA, dim**numB)) #blank coef matrix
for x in range(dim**numA):
controlA = np.array(indices[x])
for y in range(dim**numB):
for row_muA in range(dim**numA):
muA = np.array(indices[row_muA])
nuA = np.add((dim - 1) * muA, controlA) % dim
#get row corresponding to nuA
row_nuA = match_labA_to_indA(dim, nuA)
#add to coefficient
coef_mat[x, y] += (cmat_in[row_muA, y] *
cmat_in[row_nuA, y]) / (normK)
return normK, coef_mat
def P1_update_coefficients(num_nodes, dim, graph_type, cmat_in):
dim_list = list(range(dim))
numA, numB = assign_nodes(num_nodes,
graph_type) #determines node bi-partition
normK = 0
for x in range(0, dim**numA):
for y in range(0, dim**numB):
for z in range(0, y):
normK += cmat_in[x, y] * cmat_in[x, z] + cmat_in[
x, z] * cmat_in[x, y]
normK += (cmat_in[x, y])**2
#Application of measurement condition
indices = list(product(dim_list, repeat=numB))
coef_mat = np.zeros((dim**numA, dim**numB))
for x in range(dim**numA):
for y in range(dim**numB):
controlB = np.array(indices[y])
for col_muB in range(dim**numB):
muB = np.array(indices[col_muB])
nuB = np.add((dim - 1) * muB, controlB) % dim
#get col corresponding to nuB
col_nuB = match_labB_to_indB(dim, nuB)
#add to coefficient
coef_mat[x, y] += (cmat_in[x, col_muB] *
cmat_in[x, col_nuB]) / (normK)
return normK, coef_mat
def noisy_protocol_P2(num_nodes, dim, graph_type, cmat, param):
#turn one state input into two state input
cmat = np.kron(cmat, cmat)
numA, numB = assign_nodes(num_nodes,
graph_type) #determines node bi-partition
#get adj_mat
if graph_type == 'GHZ':
adj_mat = get_GHZ_adj(num_nodes)
elif graph_type == 'line':
adj_mat = get_lin_adj(num_nodes)
else:
print('Supported graph types are GHZ and line')
return
#do all noisy gates of P1
for x in range(1, num_nodes + 1):
if x <= numA:
set = 'sA'
operation = 'lower'
else:
set = 'sB'
operation = 'raise'
cmat = noisy_TQG(dim, numA, numB, adj_mat, operation, x, cmat, set,
param)
#'measure' & 'post-select' --> Use the coefficient map for general states
normK, cmat = post_measurement_state_update(
dim, numA, numB, cmat, 'P2') #input 2 states, output 1 state
return normK, cmat
def oneParam_min_fidelity(dim, num_nodes, graph_type, subP):
numA, numB = assign_nodes(num_nodes, graph_type)
if subP == 'P1':
critX = (dim**num_nodes - 2 * dim**numA + 1) / (
1 - dim**num_nodes - dim**numA + dim**(num_nodes + numA))
elif subP == 'P2':
critX = (dim**num_nodes - 2 * dim**numB + 1) / (
1 - dim**num_nodes - dim**numB + dim**(num_nodes + numB))
return critX
def single_qudit_through_channel(dim, num_nodes, graph_type, param):
numA, numB = assign_nodes(num_nodes, graph_type)
if graph_type == 'GHZ':
adj_mat = get_GHZ_adj(num_nodes)
elif graph_type == 'line':
adj_mat = get_lin_adj(num_nodes)
coef_mat = perfect_coef_mat(dim, numA, numB)
coef_mat = qudit_through_channel(dim, numA, numB, adj_mat, 1, coef_mat,
param)
return coef_mat
def state_through_channel(dim, num_nodes, graph_type, param):
numA, numB = assign_nodes(num_nodes, graph_type)
if graph_type == 'GHZ':
adj_mat = get_GHZ_adj(num_nodes)
elif graph_type == 'line':
adj_mat = get_lin_adj(num_nodes)
coef_mat = perfect_coef_mat(dim, numA, numB)
for x in range(1, num_nodes + 1):
coef_mat = qudit_through_channel(dim, numA, numB, adj_mat, x, coef_mat,
param)
return coef_mat
def get_input_coefficients(num_nodes, dim, graph_type, input_type, param):
numA, numB = assign_nodes(num_nodes, graph_type)
#set coefficients
if input_type == 'oneParam':
filename = '../oneParam_Graph_States/{}_{}_{}_{}.txt'.format(
dim, num_nodes, graph_type, param)
if os.path.isfile(filename):
coef_mat = np.loadtxt(filename).reshape(dim**numA, dim**numB)
else:
print('generate')
#rows associated with A labels
#columns with B labels
coef_mat = np.zeros((dim**numA, dim**numB))
coef_mat[0, 0] = param + (1 - param) / (dim**num_nodes)
for x in range(0, dim**numA):
for y in range(0, dim**numB):
if x == 0 and y == 0:
continue
else:
coef_mat[x, y] = (1 - param) / (dim**num_nodes)
elif input_type == 'DP':
pstring = str(param)
filename = '../Depolarized_Graph_States/{}_{}_{}_{}.txt'.format(
dim, num_nodes, graph_type, pstring)
if os.path.isfile(filename):
coef_mat = np.loadtxt(filename).reshape(dim**numA, dim**numB)
else:
coef_mat = state_through_channel(dim, num_nodes, graph_type, param)
elif input_type == 'SQWN':
pstring = str(param)
filename = '../Single_Qudit_White_Noise/{}_{}_{}_{}.txt'.format(
dim, num_nodes, graph_type, pstring)
if os.path.isfile(filename):
coef_mat = np.loadtxt(filename).reshape(dim**numA, dim**numB)
else:
coef_mat = single_qudit_through_channel(dim, num_nodes, graph_type,
param)
return coef_mat
def save_oneParam_coefficients(num_nodes, dim, graph_type, param):
numA, numB = assign_nodes(num_nodes, graph_type)
coef_mat = np.zeros((dim**numA, dim**numB))
coef_mat[0, 0] = param + (1 - param) / (dim**num_nodes)
for x in range(0, dim**numA):
for y in range(0, dim**numB):
if x == 0 and y == 0:
continue
else:
coef_mat[x, y] = (1 - param) / (dim**num_nodes)
filename = '../oneParam_Graph_States/{}_{}_{}_{}.txt'.format(
dim, num_nodes, graph_type, param)
if not os.path.isfile(filename):
afile = open(filename, 'w')
for row in coef_mat:
np.savetxt(afile, row)
afile.close()
return