def UDecompositionFullConnectivity(party_map, q, num_qubit):
'''
Naive methods for converting a party map with full connectivity
'''
debug_flag = 0
operation_CNOT = []
for colunm in range(num_qubit):
'''set diagonal entry to 1'''
if party_map[colunm][colunm] == 0:
for raw in list(range(colunm + 1, num_qubit)):
if party_map[raw][colunm] == 1:
if debug_flag == 1: print('control', raw, 'target', colunm)
PerformRawAddinPartyMap(party_map, raw, colunm)
if debug_flag == 1: print(party_map)
add_CNOT = OperationCNOT(q[raw], q[colunm])
operation_CNOT.append(add_CNOT)
break
for raw in list(range(colunm)) + list(range(colunm + 1, num_qubit)):
if party_map[raw][colunm] == 1:
if debug_flag == 1: print('control', colunm, 'target', raw)
PerformRawAddinPartyMap(party_map, colunm, raw)
if debug_flag == 1: print(party_map)
add_CNOT = OperationCNOT(q[colunm], q[raw])
operation_CNOT.append(add_CNOT)
return operation_CNOT
def RemoteCNOTinArchitectureGraph(path, party_map, q):
'''
implement remote CNOT in party map via path of nodes in architecture graph, i.e., [v_c, ..., v_t]
'''
operation_CNOT = []
dis = len(path) - 1
v_c = path[0]
v_t = path[-1]
if dis == 2:
add_CNOT = OperationCNOT(q[v_c], q[path[1]])
operation_CNOT.append(add_CNOT)
PerformRawAddinPartyMap(party_map, v_c, path[1])
add_CNOT = OperationCNOT(q[path[1]], q[v_t])
operation_CNOT.append(add_CNOT)
PerformRawAddinPartyMap(party_map, path[1], v_t)
add_CNOT = OperationCNOT(q[v_c], q[path[1]])
operation_CNOT.append(add_CNOT)
PerformRawAddinPartyMap(party_map, v_c, path[1])
add_CNOT = OperationCNOT(q[path[1]], q[v_t])
operation_CNOT.append(add_CNOT)
PerformRawAddinPartyMap(party_map, path[1], v_t)
else:
if dis == 3:
add_CNOT = OperationCNOT(q[v_c], q[path[1]])
operation_CNOT.append(add_CNOT)
PerformRawAddinPartyMap(party_map, v_c, path[1])
add_CNOT = OperationCNOT(q[path[2]], q[v_t])
operation_CNOT.append(add_CNOT)
PerformRawAddinPartyMap(party_map, path[2], v_t)
add_CNOT = OperationCNOT(q[path[1]], q[path[2]])
operation_CNOT.append(add_CNOT)
PerformRawAddinPartyMap(party_map, path[1], path[2])
add_CNOT = OperationCNOT(q[v_c], q[path[1]])
operation_CNOT.append(add_CNOT)
PerformRawAddinPartyMap(party_map, v_c, path[1])
add_CNOT = OperationCNOT(q[path[1]], q[path[2]])
operation_CNOT.append(add_CNOT)
PerformRawAddinPartyMap(party_map, path[1], path[2])
else:
'''See Section 2B , arXiv:1904.01972'''
'''first part'''
for i in range(dis):
R = []
add_CNOT = OperationCNOT(q[path[-1 - i - i]], q[path[-1 - i]])
R.append(add_CNOT)
R_prime = copy.deepcopy(R_operation)
R_prime.pop()
R_prime.reverse()
operation_CNOT.extend(R + R_prime)
R_star = copy.deepcopy(R + R_prime)
R_star.pop()
R_star.pop(0)
operation_CNOT.extend(R_star)
return operation_CNOT
def FillSteinerTreeRootToLeaf(q, steiner_tree, party_map, terminal_nodes,
shortest_path_steiner_tree):
'''
Use CNOT operation to set all nodes in steiner tree 1 from root to leaf
Refresh party map
Return:
list of CNOT operations
'''
operation_CNOT = []
num_leaf = len(terminal_nodes) - 1
root_node = terminal_nodes[0]
for i in range(num_leaf):
leaf_node = terminal_nodes[i + 1]
path = shortest_path_steiner_tree[leaf_node][root_node]
l = len(path)
for current_pos in range(l - 2, -1, -1):
current_node = path[current_pos]
son_node = path[current_pos + 1]
if steiner_tree.node[current_node]['party_map_value'] == 0:
add_CNOT = OperationCNOT(q[son_node], q[current_node])
operation_CNOT.append(add_CNOT)
party_map[current_node][:] = np.logical_xor(
party_map[current_node][:], party_map[son_node][:])
steiner_tree.node[current_node]['party_map_value'] = 1
return operation_CNOT
def QiskitGateToOperation(Gate):
'''
convert a Qiskit Gate object to OperationU
only support CNOT
'''
if Gate.name == 'cx':
qargs = Gate.qargs
return OperationCNOT(qargs[0], qargs[1])
return None
def EmptySteinerTree(q, steiner_tree, party_map, terminal_nodes):
operation_CNOT = []
DFT_edges = list(nx.dfs_edges(steiner_tree, source=terminal_nodes[0]))
DFT_edges.reverse()
for edge in DFT_edges:
current_node = edge[0]
son_node = edge[1]
add_CNOT = OperationCNOT(q[current_node], q[son_node])
operation_CNOT.append(add_CNOT)
party_map[son_node][:] = np.logical_xor(party_map[current_node][:],
party_map[son_node][:])
steiner_tree.node[son_node]['party_map_value'] = 1
return operation_CNOT
def UDecompositionFullConnectivityPATEL(party_map, q, num_qubit, m=None):
'''
Optimal methods for converting a party map with full connectivity
Using partition
See "OPTIMAL SYNTHESIS OF LINEAR REVERSIBLE CIRCUITS"
'''
operation_CNOT = []
'''set value of m'''
if m == None:
cuurent_m = int(np.log2(num_qubit))
while int(num_qubit / cuurent_m) != (num_qubit / cuurent_m):
cuurent_m -= 1
m = cuurent_m
'''transform to upper triangle'''
'''traverse all sections'''
for start_col in range(0, num_qubit, m):
list_all_col = list(range(start_col, start_col + m))
'''delete duplicate sub-rows'''
for raw in list_all_col:
module = party_map[raw][list_all_col]
if np.sum(module) > 1:
for raw2 in range(list_all_col[-1] + 1, num_qubit):
module2 = party_map[raw2][list_all_col]
if np.array_equal(module, module2) == True:
PerformRawAddinPartyMap(party_map, raw, raw2)
add_CNOT = OperationCNOT(q[raw], q[raw2])
operation_CNOT.append(add_CNOT)
'''set values of all entries in each column of current subsection'''
for current_col_sec in list_all_col:
'''set diagonal entry to 1'''
if party_map[current_col_sec][current_col_sec] != 1:
for i in range(current_col_sec + 1, num_qubit):
if party_map[i][current_col_sec] == 1:
PerformRawAddinPartyMap(party_map, i, current_col_sec)
add_CNOT = OperationCNOT(q[i], q[current_col_sec])
operation_CNOT.append(add_CNOT)
break
'''set other entries in this column'''
for current_raw in range(current_col_sec + 1, num_qubit):
if party_map[current_raw][current_col_sec] == 1:
PerformRawAddinPartyMap(party_map, current_col_sec,
current_raw)
add_CNOT = OperationCNOT(q[current_col_sec],
q[current_raw])
operation_CNOT.append(add_CNOT)
'''transform to upper identity'''
'''traverse all sections'''
for start_col in range(num_qubit - 1, -1, -1 * m):
list_all_col = list(range(start_col, start_col - m, -1))
'''delete duplicate sub-rows'''
for raw in list_all_col:
module = party_map[raw][list_all_col]
if np.sum(module) > 1:
for raw2 in range(list_all_col[-1] - 1, -1, -1):
module2 = party_map[raw2][list_all_col]
if np.array_equal(module, module2) == True:
PerformRawAddinPartyMap(party_map, raw, raw2)
add_CNOT = OperationCNOT(q[raw], q[raw2])
operation_CNOT.append(add_CNOT)
'''set values of all entries in each column of current subsection'''
for current_col_sec in list_all_col:
'''set diagonal entry to 1'''
if party_map[current_col_sec][current_col_sec] != 1:
for i in range(current_col_sec - 1, -1, -1):
if party_map[i][current_col_sec] == 1:
PerformRawAddinPartyMap(party_map, i, current_col_sec)
add_CNOT = OperationCNOT(q[i], q[current_col_sec])
operation_CNOT.append(add_CNOT)
break
'''set other entries in this column'''
for current_raw in range(current_col_sec - 1, -1, -1):
if party_map[current_raw][current_col_sec] == 1:
PerformRawAddinPartyMap(party_map, current_col_sec,
current_raw)
add_CNOT = OperationCNOT(q[current_col_sec],
q[current_raw])
operation_CNOT.append(add_CNOT)
return operation_CNOT
def EliminateOneEntryInColumn(party_map, steiner_tree_total, sub_steiner_trees,
sub_trees_root_node, terminal_nodes, q):
'''
See chapter 4.1, arXiv:1904.01972
'''
flag_debug = 0
operation_CNOT = []
for i in range(len(sub_steiner_trees)):
'''if root node of a sub Steiner tree is not the biggest'''
current_tree = sub_steiner_trees[i]
current_root = sub_trees_root_node[i]
leaf_nodes = FindAllLeafNodesInTree(current_tree)
if current_root < max(leaf_nodes):
#print('testing')
add_operations = EliminateOneEntryInColumn(party_map,
steiner_tree_total,
[steiner_tree_total],
[max(terminal_nodes)],
terminal_nodes, q)
operation_CNOT.extend(add_operations)
return operation_CNOT
'''else'''
for i in range(len(sub_steiner_trees)):
tree = sub_steiner_trees[i]
root_node = sub_trees_root_node[i]
R_operation = []
shortest_length_tree = dict(
nx.shortest_path_length(tree,
source=None,
target=None,
weight=None,
method='dijkstra'))
BFS_edges = list(nx.bfs_edges(tree, source=root_node))
BFS_edges.reverse()
if flag_debug == 1: print('BFS edges are', BFS_edges)
for edge in BFS_edges:
if shortest_length_tree[edge[0]][root_node] < shortest_length_tree[
edge[1]][root_node]:
control_q = q[edge[0]]
target_q = q[edge[1]]
else:
control_q = q[edge[1]]
target_q = q[edge[0]]
R_operation.append(OperationCNOT(control_q, target_q))
'''calculate R_prime'''
R_prime = copy.deepcopy(R_operation)
'''delete redundancy of R_prime'''
for operation in copy.copy(R_prime):
if operation.control_qubit[1] == root_node:
R_prime.remove(operation)
#R_prime.pop()
R_prime.reverse()
'''calculate R_star'''
add_R_star = []
leaf_nodes = FindAllLeafNodesInTree(tree)
R_star = copy.deepcopy(R_operation) + copy.deepcopy(R_prime)
for operation in copy.copy(R_star):
if (operation.target_qubit[1]
in terminal_nodes) and (operation.target_qubit[1]
in leaf_nodes):
R_star.remove(operation)
'''这个部分不正确，但是可以用来预估增加的CNOT数目'''
if (operation.target_qubit[1] in terminal_nodes) and (
not operation.target_qubit[1] in leaf_nodes):
add_R_star.append(
OperationCNOT(operation.target_qubit,
operation.control_qubit))
add_R_star_copy = copy.deepcopy(add_R_star)
add_R_star_copy.reverse()
if add_R_star != []: R_star = add_R_star + R_star + add_R_star_copy
'''total operation'''
R_total = R_operation + R_prime + R_star
operation_CNOT.extend(R_total)
if flag_debug == 1: print('R_operation')
PerformOperationCNOTinPartyMap(party_map, R_operation)
if flag_debug == 1: print('R_prime')
PerformOperationCNOTinPartyMap(party_map, R_prime)
if flag_debug == 1: print('R_star')
PerformOperationCNOTinPartyMap(party_map, R_star)
#PerformOperationCNOTinPartyMap(party_map, R_total)
return operation_CNOT