def get_upper_bound_peo(graph, method='tamaki', **kwargs):
"""
Run one of the heuristics to get PEO and treewidth
Parameters:
-----------
graph: networkx.Graph
graph to calculate PEO
method: str, default 'tamaki'
solver to use
**kwargs: default {}
optional keyword arguments to pass to the solver
"""
builtin_heuristics = {"min_fill", "min_degree", "cardinality"}
pace_heuristics = {"tamaki"}
if method in pace_heuristics:
peo, tw = get_upper_bound_peo_pace2017(graph, method, **kwargs)
elif method in builtin_heuristics:
peo, tw = get_upper_bound_peo_builtin(graph, method)
elif method == "quickbb":
peo, tw = get_upper_bound_peo_quickbb(graph, **kwargs)
else:
raise ValueError(f'Unknown method: {method}')
peo_vars = [
Var(var, size=graph.nodes[var]['size'], name=graph.nodes[var]['name'])
for var in peo
]
return peo_vars, tw
def nodes_to_vars(old_graph, peo):
peo_vars = [
Var(v,
size=old_graph.nodes[v]['size'],
name=old_graph.nodes[v]['name']) for v in peo
]
return peo_vars
def get_peo(old_graph, method="tamaki"):
"""
Calculates a perfect elimination order using one of the
external methods.
Parameters
----------
graph : networkx.Graph
graph to estimate
method : str
one of {"tamaki"}
Returns
-------
peo : list
list of nodes in perfect elimination order
treewidth : int
treewidth corresponding to peo
"""
from qtree.graph_model.clique_trees import get_peo_from_tree
import qtree.graph_model.pace2017_solver_api as api
method_args = {
'tamaki': {
'command': './tw-exact',
'cwd': defs.TAMAKI_SOLVER_PATH
}
}
assert (method in method_args.keys())
# ensure graph is labeled starting from 1 with integers
graph, inv_dict = relabel_graph_nodes(
old_graph,
dict(zip(old_graph.nodes, range(1,
old_graph.number_of_nodes() + 1))))
# Remove selfloops and parallel edges. Critical
graph = get_simple_graph(graph)
data = generate_gr_file(graph)
out_data = api.run_exact_solver(data, **method_args[method])
tree, treewidth = read_td_file(out_data, as_data=True)
peo = get_peo_from_tree(tree)
peo = [inv_dict[pp] for pp in peo]
try:
peo_vars = [
Var(var,
size=old_graph.nodes[var]['size'],
name=old_graph.nodes[var]['name']) for var in peo
]
except:
peo_vars = peo
return peo_vars, treewidth
def split_graph_random(old_graph, n_var_parallel=0):
"""
Splits a graphical model with randomly chosen nodes
to parallelize over.
Parameters
----------
old_graph : networkx.Graph
graph to contract (after eliminating variables which
are parallelized over)
n_var_parallel : int
number of variables to eliminate by parallelization
Returns
-------
idx_parallel : list of Idx
variables removed by parallelization
graph : networkx.Graph
new graph without parallelized variables
"""
graph = copy.deepcopy(old_graph)
indices = [var for var in graph.nodes(data=False)]
idx_parallel = np.random.choice(
indices, size=n_var_parallel, replace=False)
idx_parallel_var = [Var(var, size=graph.nodes[var])
for var in idx_parallel]
for idx in idx_parallel:
remove_node(graph, idx)
log.info("Removed indices by parallelization:\n{}".format(idx_parallel))
log.info("Removed {} variables".format(len(idx_parallel)))
peo, treewidth = get_peo(graph)
return sorted(idx_parallel_var, key=int), graph
def maximum_cardinality_search(old_graph, last_clique_vertices=[]):
"""
This function builds elimination order of a chordal graph
using maximum cardinality search algorithm.
If last_clique_vertices is
provided the algorithm will place these indices at the end
of the elimination list in the same order as provided.
Parameters
----------
graph : nx.Graph or nx.MultiGraph
chordal graph to build the elimination order
last_clique_vertices : list, default []
list of vertices to be placed at the end of
the elimination order
Returns
-------
list
Perfect elimination order
"""
# convert input to int
last_clique_vertices = [int(var) for var in last_clique_vertices]
# Check is last_clique_vertices is a clique
graph = copy.deepcopy(old_graph)
n_nodes = graph.number_of_nodes()
nodes_number_of_ord_neighbors = {node: 0 for node in graph.nodes}
# range(0, n_nodes + 1) is important here as we need n+1 lists
# to ensure proper indexing in the case of a clique
nodes_by_ordered_neighbors = [[] for ii in range(0, n_nodes + 1)]
for node in graph.nodes:
nodes_by_ordered_neighbors[0].append(node)
last_nonempty = 0
peo = []
for ii in range(n_nodes, 0, -1):
# Take any unordered node with highest cardinality
# or the ones in the last_clique_vertices if it was provided
if len(last_clique_vertices) > 0:
# Forcibly select the node from the clique
node = last_clique_vertices.pop()
# The following should always be possible if
# last_clique_vertices induces a clique and I understood
# the theorem correctly. If it raises something is wrong
# with the algorithm/input is not a clique
try:
nodes_by_ordered_neighbors[last_nonempty].remove(node)
except ValueError:
if not is_clique(graph, last_clique_vertices):
raise ValueError('last_clique_vertices are not a clique')
else:
raise AssertionError('Algorithmic error. Investigate')
else:
node = nodes_by_ordered_neighbors[last_nonempty].pop()
peo = [node] + peo
nodes_number_of_ord_neighbors[node] = -1
unordered_neighbors = [(neighbor,
nodes_number_of_ord_neighbors[neighbor])
for neighbor in graph[node]
if nodes_number_of_ord_neighbors[neighbor] >= 0]
# Increase number of ordered neighbors for all adjacent
# unordered nodes
for neighbor, n_ordered_neighbors in unordered_neighbors:
nodes_by_ordered_neighbors[n_ordered_neighbors].remove(neighbor)
nodes_number_of_ord_neighbors[neighbor] = (n_ordered_neighbors + 1)
nodes_by_ordered_neighbors[n_ordered_neighbors +
1].append(neighbor)
last_nonempty += 1
while last_nonempty >= 0:
if len(nodes_by_ordered_neighbors[last_nonempty]) == 0:
last_nonempty -= 1
else:
break
# Create Var objects
peo_vars = [
Var(var, size=graph.nodes[var]['size'], name=graph.nodes[var]['name'])
for var in peo
]
return peo_vars
def circ2graph(qubit_count,
circuit,
pdict={},
max_depth=None,
omit_terminals=True):
"""
Constructs a graph from a circuit in the form of a
list of lists.
Parameters
----------
qubit_count : int
number of qubits in the circuit
circuit : list of lists
quantum circuit as returned by
:py:meth:`operators.read_circuit_file`
pdict : dict
Dictionary with placeholders if any parameteric gates
were unresolved
max_depth : int, default None
Maximal depth of the circuit which should be used
omit_terminals : bool, default True
If terminal nodes should be excluded from the final
graph.
Returns
-------
graph : networkx.MultiGraph
Graph which corresponds to the circuit
data_dict : dict
Dictionary with all tensor data
"""
import functools
import qtree.operators as ops
if max_depth is None:
max_depth = len(circuit)
data_dict = {}
# Let's build the graph.
# The circuit is built from left to right, as it operates
# on the ket ( |0> ) from the left. We thus first place
# the bra ( <x| ) and then put gates in the reverse order
# Fill the variable `frame`
layer_variables = list(range(qubit_count))
current_var_idx = qubit_count
# Initialize the graph
graph = nx.MultiGraph()
# Populate nodes and save variables of the bra
bra_variables = []
for var in layer_variables:
graph.add_node(var, name=f'o_{var}', size=2)
bra_variables.append(Var(var, name=f"o_{var}"))
# Place safeguard measurement circuits before and after
# the circuit
measurement_circ = [[ops.M(qubit) for qubit in range(qubit_count)]]
combined_circ = functools.reduce(
lambda x, y: itertools.chain(x, y),
[measurement_circ, reversed(circuit[:max_depth])])
# Start building the graph in reverse order
for layer in combined_circ:
for op in layer:
# build the indices of the gate. If gate
# changes the basis of a qubit, a new variable
# has to be introduced and current_var_idx is increased.
# The order of indices
# is always (a_new, a, b_new, b, ...), as
# this is how gate tensors are chosen to be stored
variables = []
current_var_idx_copy = current_var_idx
for qubit in op.qubits:
if qubit in op.changed_qubits:
variables.extend(
[layer_variables[qubit], current_var_idx_copy])
graph.add_node(current_var_idx_copy,
name='v_{}'.format(current_var_idx_copy),
size=2)
current_var_idx_copy += 1
else:
variables.extend([layer_variables[qubit]])
# Form a tensor and add a clique to the graph
# fill placeholders in gate's parameters if any
for par, value in op.parameters.items():
if isinstance(value, ops.placeholder):
op._parameters[par] = pdict[value]
data_key = hash((op.name, tuple(op.parameters.items())))
tensor = {
'name': op.name,
'indices': tuple(variables),
'data_key': data_key
}
# Insert tensor data into data dict
data_dict[data_key] = op.gen_tensor()
if len(variables) > 1:
edges = itertools.combinations(variables, 2)
else:
edges = [(variables[0], variables[0])]
graph.add_edges_from(edges, tensor=tensor)
# Update current variable frame
for qubit in op.changed_qubits:
layer_variables[qubit] = current_var_idx
current_var_idx += 1
# Finally go over the qubits, append measurement gates
# and collect ket variables
ket_variables = []
op = ops.M(0) # create a single measurement gate object
for qubit in range(qubit_count):
var = layer_variables[qubit]
new_var = current_var_idx
ket_variables.append(Var(new_var, name=f'i_{qubit}', size=2))
# update graph and variable `frame`
graph.add_node(new_var, name=f'i_{qubit}', size=2)
data_key = hash((op.name, tuple(op.parameters.items())))
tensor = {
'name': op.name,
'indices': (var, new_var),
'data_key': data_key
}
graph.add_edge(var, new_var, tensor=tensor)
layer_variables[qubit] = new_var
current_var_idx += 1
if omit_terminals:
graph.remove_nodes_from(tuple(map(int, bra_variables + ket_variables)))
v = graph.number_of_nodes()
e = graph.number_of_edges()
log.info(f"Generated graph with {v} nodes and {e} edges")
# log.info(f"last index contains from {layer_variables}")
return graph, data_dict, bra_variables, ket_variables
def split_graph_by_metric_greedy(
old_graph, n_var_parallel=0,
metric_fn=get_node_by_treewidth_reduction,
greedy_step_by=1, forbidden_nodes=(), peo_function=get_peo):
"""
This function splits graph by greedily selecting next nodes
up to the n_var_parallel
using the metric function and recomputing PEO after
each node elimination
Parameters
----------
old_graph : networkx.Graph or networkx.MultiGraph
graph to split by parallelizing over variables
and to contract
Parallel edges and self-loops in the graph are
removed (if any) before the calculation of metric
n_var_parallel : int
number of variables to eliminate by parallelization
metric_fn : function, optional
function to evaluate node metric.
Default get_node_by_mem_reduction
greedy_step_by : int, default 1
Step size for the greedy algorithm
forbidden_nodes : iterable, optional
nodes in this list will not be considered
for deletion. Default ().
peo_function: function
function to calculate PEO. Should have signature
lambda (graph): return peo, treewidth
Returns
-------
idx_parallel : list
variables removed by parallelization
graph : networkx.Graph
new graph without parallelized variables
"""
# import pdb
# pdb.set_trace()
# convert everything to int
forbidden_nodes = [int(var) for var in forbidden_nodes]
# Simplify graph
graph = get_simple_graph(old_graph)
idx_parallel = []
idx_parallel_var = []
steps = [greedy_step_by] * (n_var_parallel // greedy_step_by)
# append last batch to steps
steps.append(n_var_parallel
- (n_var_parallel // greedy_step_by) * greedy_step_by)
for n_parallel in steps:
# Get optimal order - recalculate treewidth
peo, tw = peo_function(graph)
graph_optimal, inverse_order = relabel_graph_nodes(
graph, dict(zip(peo, sorted(graph.nodes))))
# get nodes by metric in descending order
nodes_by_metric_optimal = metric_fn(graph_optimal)
nodes_by_metric_optimal.sort(
key=lambda pair: pair[1], reverse=True)
# filter out forbidden nodes and get nodes in original order
nodes_by_metric_allowed = []
for node, metric in nodes_by_metric_optimal:
if inverse_order[node] not in forbidden_nodes:
nodes_by_metric_allowed.append(
(inverse_order[node], metric))
# Take first nodes by cost and map them back to original
# order
nodes_with_cost = nodes_by_metric_allowed[:n_parallel]
if len(nodes_with_cost) > 0:
nodes, costs = zip(*nodes_with_cost)
else:
nodes = []
# Update list and update graph
idx_parallel += nodes
# create var objects from nodes
idx_parallel_var += [Var(var, size=graph.nodes[var]['size'])
for var in nodes]
for node in nodes:
remove_node(graph, node)
return idx_parallel_var, graph
def split_graph_with_mem_constraint_greedy(
old_graph,
n_var_parallel_min=0,
mem_constraint=defs.MAXIMAL_MEMORY,
step_by=5,
n_var_parallel_max=None,
metric_fn=get_node_by_mem_reduction,
forbidden_nodes=(),
peo_function=get_peo):
"""
This function splits graph by greedily selecting next nodes
up to the n_var_parallel
using the metric function and recomputing PEO after
each node elimination. The graph is **ASSUMED** to be in
the perfect elimination order
Parameters
----------
old_graph : networkx.Graph()
initial contraction graph
n_var_parallel_min : int
minimal number of variables to split the task to
mem_constraint : int
Upper limit on memory per task
metric_function : function, optional
function to rank nodes for elimination
step_by : int, optional
scan the metric function with this step
n_var_parallel_max : int, optional
constraint on the maximal number of parallelized
variables. Default None
forbidden_nodes: iterable, default ()
nodes forbidden for parallelization
peo_function: function
function to calculate PEO. Should have signature
lambda (graph): return peo, treewidth
Returns
-------
idx_parallel : list
list of removed variables
graph : networkx.Graph
reduced contraction graph
"""
# convert everything to int
forbidden_nodes = [int(var) for var in forbidden_nodes]
graph = copy.deepcopy(old_graph)
n_var_total = old_graph.number_of_nodes()
if n_var_parallel_max is None:
n_var_parallel_max = n_var_total
mem_cost, flop_cost = get_contraction_costs(graph)
max_mem = sum(mem_cost)
idx_parallel = []
idx_parallel_var = []
steps = list(range(0, n_var_parallel_max, step_by))
if len(steps) == 0 or (n_var_parallel_max % step_by != 0):
steps.append(n_var_parallel_max)
steps = [step_by] * (n_var_parallel_max // step_by)
# append last batch to steps
steps.append(n_var_parallel_max
- (n_var_parallel_max // step_by) * step_by)
for n_parallel in steps:
# Get optimal order
peo, tw = peo_function(graph)
graph_optimal, inverse_order = relabel_graph_nodes(
graph, dict(zip(peo, range(len(peo)))))
# get nodes by metric in descending order
nodes_by_metric_optimal = metric_fn(graph_optimal)
nodes_by_metric_optimal.sort(
key=lambda pair: pair[1], reverse=True)
nodes_by_metric_allowed = []
for node, metric in nodes_by_metric_optimal:
if inverse_order[node] not in forbidden_nodes:
nodes_by_metric_allowed.append(
(inverse_order[node], metric))
# Take first nodes by cost and map them back to original
# order
nodes_with_cost = nodes_by_metric_allowed[:n_parallel]
if len(nodes_with_cost) > 0:
nodes, costs = zip(*nodes_with_cost)
else:
nodes = []
# Update list and update graph
idx_parallel += nodes
# create var objects from nodes
idx_parallel_var += [Var(var, size=graph.nodes[var]['size'])
for var in nodes]
for node in nodes:
remove_node(graph, node)
# Renumerate graph nodes to be consequtive ints (may be redundant)
label_dict = dict(zip(sorted(graph.nodes),
range(len(graph.nodes()))))
graph_relabelled, _ = relabel_graph_nodes(graph, label_dict)
mem_cost, flop_cost = get_contraction_costs(graph_relabelled)
max_mem = sum(mem_cost)
if (max_mem <= mem_constraint
and len(idx_parallel) >= n_var_parallel_min):
break
if max_mem > mem_constraint:
raise ValueError('Maximal memory constraint is not met')
return idx_parallel_var, graph
def split_graph_by_metric(
old_graph, n_var_parallel=0,
metric_fn=get_node_by_degree,
forbidden_nodes=()):
"""
Parallel-splitted version of :py:meth:`get_peo` with nodes
to split chosen according to the metric function. Metric
function should take a graph and return a list of pairs
(node : metric_value)
Parameters
----------
old_graph : networkx.Graph or networkx.MultiGraph
graph to split by parallelizing over variables
and to contract
Parallel edges and self-loops in the graph are
removed (if any) before the calculation of metric
n_var_parallel : int
number of variables to eliminate by parallelization
metric_fn : function, optional
function to evaluate node metric.
Default get_node_by_degree
forbidden_nodes : iterable, optional
nodes in this list will not be considered
for deletion. Default ().
Returns
-------
idx_parallel : list
variables removed by parallelization
graph : networkx.Graph
new graph without parallelized variables
"""
# graph = get_simple_graph(old_graph)
# import pdb
# pdb.set_trace()
graph = copy.deepcopy(old_graph)
# convert everything to int
forbidden_nodes = [int(var) for var in forbidden_nodes]
# get nodes by metric in descending order
nodes_by_metric = metric_fn(graph)
nodes_by_metric.sort(key=lambda pair: int(pair[1]), reverse=True)
nodes_by_metric_allowed = []
for node, metric in nodes_by_metric:
if node not in forbidden_nodes:
nodes_by_metric_allowed.append((node, metric))
idx_parallel = []
for ii in range(n_var_parallel):
node, metric = nodes_by_metric_allowed[ii]
idx_parallel.append(node)
# create var objects from nodes
idx_parallel_var = [Var(var, size=graph.nodes[var]['size'])
for var in idx_parallel]
for idx in idx_parallel:
remove_node(graph, idx)
log.info("Removed indices by parallelization:\n{}".format(idx_parallel))
log.info("Removed {} variables".format(len(idx_parallel)))
return idx_parallel_var, graph