def output_dw(outfile, problem):
"Output weights and strengths in dw format."
if not problem.qubo:
qprob = problem.convert_to_qubo()
output_weights, output_strengths = qprob.weights, qprob.strengths
else:
output_weights = problem.weights
output_strengths = problem.strengths
try:
L, M, N = qmasm.chimera_topology(qmasm.solver)
except qmasm.NonChimera:
qmasm.abend("dw output is supported only for Chimera-graph topologies")
wdata = []
for q in range(len(output_weights)):
if output_weights[q] != 0.0:
wdata.append("Q%0d <== %.25g" % (q, output_weights[q]))
wdata.sort()
sdata = []
for sp, str in output_strengths.items():
if str != 0.0:
try:
coupler = coupler_number(M, N, L, sp[0], sp[1])
except IndexError:
qmasm.abend("dw output is supported only for Chimera-graph topologies")
sdata.append("C%04d <== %.25g" % (coupler, str))
sdata.sort()
outfile.write("\n".join(wdata + sdata) + "\n")
def output_dw(outfile, problem):
"Output weights and strengths in dw format."
if not problem.qubo:
qprob = problem.convert_to_qubo()
output_weights, output_strengths = qprob.weights, qprob.strengths
else:
output_weights = problem.weights
output_strengths = problem.strengths
try:
L, M, N = qmasm.chimera_topology(qmasm.solver)
except qmasm.NonChimera:
qmasm.abend("dw output is supported only for Chimera-graph topologies")
wdata = []
for q in range(len(output_weights)):
if output_weights[q] != 0.0:
wdata.append("Q%0d <== %.25g" % (q, output_weights[q]))
wdata.sort()
sdata = []
for sp, str in output_strengths.items():
if str != 0.0:
try:
coupler = coupler_number(M, N, L, sp[0], sp[1])
except IndexError:
qmasm.abend("dw output is supported only for Chimera-graph topologies")
sdata.append("C%04d <== %.25g" % (coupler, str))
sdata.sort()
outfile.write("\n".join(wdata + sdata) + "\n")
def output_dw(outfile, problem):
"Output weights and strengths in dw format."
if not problem.qubo:
qprob = problem.convert_to_qubo()
output_weights, output_strengths = qprob.weights, qprob.strengths
else:
output_weights = problem.weights
output_strengths = problem.strengths
try:
L, M, N = qmasm.chimera_topology(qmasm.solver)
except KeyError:
qmasm.abend("Failed to query the chimera topology")
wdata = []
for q in range(len(output_weights)):
if output_weights[q] != 0.0:
wdata.append("Q%0d <== %.25g" % (q, output_weights[q]))
wdata.sort()
sdata = []
for sp, str in list(output_strengths.items()):
if str != 0.0:
coupler = coupler_number(M, N, L, sp[0], sp[1])
sdata.append("C%04d <== %.25g" % (coupler, str))
sdata.sort()
outfile.write("\n".join(wdata + sdata) + "\n")
def output_bqpjson(outfile, as_qubo, problem):
"Output weights and strengths in bqpjson format, either Ising or QUBO."
# Prepare the "easy" fields.
bqp = {}
bqp["version"] = "1.0.0"
bqp["id"] = random.randint(2**20, 2**60)
bqp["scale"] = 1.0
bqp["offset"] = 0.0
if as_qubo:
bqp["variable_domain"] = "boolean"
else:
bqp["variable_domain"] = "spin"
# Prepare the list of all variables.
var_ids = set(problem.weights.keys())
for q1, q2 in problem.strengths.keys():
var_ids.add(q1)
var_ids.add(q2)
bqp["variable_ids"] = sorted(var_ids)
# Prepare the linear terms.
lin_terms = []
for q, wt in sorted(problem.weights.items()):
lin_terms.append({
"id": q,
"coeff": wt})
bqp["linear_terms"] = lin_terms
# Prepare the quadratic terms.
quad_terms = []
strengths = qmasm.canonicalize_strengths(problem.strengths)
for (q1, q2), wt in sorted(strengths.items()):
quad_terms.append({
"id_tail": q1,
"id_head": q2,
"coeff": wt})
bqp["quadratic_terms"] = quad_terms
# Prepare some metadata.
metadata = {}
if as_qubo:
metadata["description"] = "QUBO problem compiled by QMASM (https://github.com/lanl/qmasm)"
else:
metadata["description"] = "Ising problem compiled by QMASM (https://github.com/lanl/qmasm)"
metadata["command_line"] = qmasm.get_command_line()
metadata["generated"] = datetime.datetime.utcnow().isoformat()
if hasattr(problem, "embedding"):
# Physical problem
def attempt_assign(key, func):
"Try assigning a key, but don't complain if we can't."
try:
metadata[key] = func()
except KeyError:
pass
attempt_assign("dw_url", lambda: os.environ["DW_INTERNAL__HTTPLINK"])
attempt_assign("dw_solver_name", lambda: qmasm.solver_name)
props = qmasm.solver.properties
attempt_assign("dw_chip_id", lambda: props["chip_id"])
L, M, N = qmasm.chimera_topology(qmasm.solver)
metadata["chimera_cell_size"] = L*2
metadata["chimera_degree"] = max(M, N)
metadata["equivalent_ids"] = sorted(problem.chains)
metadata["variable_names"] = {s: problem.embedding[n]
for s, n in qmasm.sym_map.symbol_number_items()}
else:
metadata["variable_names"] = {s: [n]
for s, n in qmasm.sym_map.symbol_number_items()}
bqp["metadata"] = metadata
# Output the problem in JSON format.
outfile.write(json.dumps(bqp, indent=2, sort_keys=True) + "\n")
def find_dwave_embedding(logical, optimization, verbosity, hw_adj_file):
"""Find an embedding of a logical problem in the D-Wave's physical topology.
Store the embedding within the Problem object."""
# SAPI tends to choke when embed_problem is told to embed a problem
# containing a zero-weight node whose adjacent couplers all have zero
# strength. (Tested with SAPI 2.4.) To help out SAPI, we simply remove
# all zero-strength couplers.
edges = [
e for e in logical.strengths.keys() if logical.strengths[e] != 0.0
]
edges.sort()
logical.edges = edges
if hw_adj_file == None:
try:
hw_adj = get_hardware_adjacency(qmasm.solver)
except KeyError:
# The Ising heuristic solver is an example of a solver that lacks a
# fixed hardware representation. We therefore assert that the
# hardware is an all-to-all network that connects every node to
# every other node.
endpoints = set([a for a, b in edges] + [b for a, b in edges])
hw_adj = [(a, b) for a in endpoints for b in endpoints if a != b]
else:
hw_adj = read_hardware_adjacency(hw_adj_file, verbosity)
# Tell the user if we have any hope at all of embedding the problem.
if verbosity >= 2:
report_embeddability(edges, hw_adj)
# Determine the edges of a rectangle of cells we want to use. If we read
# the topology from a file or otherwise can't prove that we have a Chimera
# graph, we call this rectangle 0x0 and force the main embedding loop to
# exit after a single iteration because we don't know the topology is even
# rectangular.
edgex = 0
edgey = 0
M = 0
N = 0
try:
if hw_adj_file == None:
L, M, N = qmasm.chimera_topology(qmasm.solver)
L2 = 2 * L
ncells = (qmasm.next_sym_num +
L2) // L2 # Round up the number of cells.
if optimization >= 2:
edgey = max(int(math.sqrt(ncells)), 1)
edgex = max((ncells + edgey - 1) // edgey, 1)
else:
edgey = N
edgex = M
except qmasm.NonChimera:
pass
# Announce what we're about to do.
if verbosity >= 2:
sys.stderr.write(
"Embedding the logical adjacency within the physical topology.\n\n"
)
# Repeatedly expand edgex and edgey until the embedding works.
while edgex <= M and edgey <= N:
if edgex == M and edgey == N:
alt_hw_adj = hw_adj
else:
# Retain adjacencies only within the rectangle.
alt_hw_adj = []
for q1, q2 in hw_adj:
c1 = q1 // L2
if c1 % M >= edgex:
continue
if c1 // M >= edgey:
continue
c2 = q2 // L2
if c2 % M >= edgex:
continue
if c2 // M >= edgey:
continue
alt_hw_adj.append((q1, q2))
alt_hw_adj = set(alt_hw_adj)
logical.hw_adj = alt_hw_adj
# See if we already have an embedding in the embedding cache.
ec = EmbeddingCache(edges, alt_hw_adj)
if verbosity >= 2:
if ec.cachedir == None:
sys.stderr.write(
" No embedding cache directory was specified ($QMASMCACHE).\n"
)
else:
sys.stderr.write(
" Using %s as the embedding cache directory ...\n" %
ec.cachedir)
embedding = ec.read()
if embedding == []:
# Cache hit, but embedding had failed
if verbosity >= 2:
sys.stderr.write(
" Found failed embedding %s in the embedding cache.\n\n" %
ec.hash)
elif embedding != None:
# Successful cache hit!
if verbosity >= 2:
sys.stderr.write(
" Found successful embedding %s in the embedding cache.\n\n"
% ec.hash)
logical.embedding = embedding
return
if verbosity >= 2 and ec.cachedir != None:
sys.stderr.write(
" No existing embedding found in the embedding cache.\n")
# Try to find an embedding, unless we previously determined that it had
# failed.
if embedding != []:
if verbosity >= 2:
# SAPI's find_embedding is hard-wired to write to stdout.
# Trick it into writing into a pipe instead.
if edgex == 0 and edgey == 0:
sys.stderr.write(" Trying to embed ... ")
else:
sys.stderr.write(
" Trying a %dx%d unit-cell embedding ...\n\n" %
(edgex, edgey))
sepLine = "=== EMBEDDING ===\n"
r, w = os.pipe()
pid = os.fork()
if pid == 0:
# Child -- perform the embedding.
os.close(r)
os.dup2(w, sys.stdout.fileno())
embedding = find_embedding(edges, alt_hw_adj, verbose=1)
sys.stdout.flush()
os.write(w, sepLine)
os.write(w, json.dumps(embedding) + "\n")
os.close(w)
os._exit(0)
else:
# Parent -- report the embedding's progress.
os.close(w)
pipe = os.fdopen(r, "r", 10000)
while True:
try:
rstr = pipe.readline()
if rstr == sepLine:
break
if rstr == "":
qmasm.abend(
"Embedder failed to terminate properly")
sys.stderr.write(" %s" % rstr)
except:
pass
# Receive the embedding from the child.
embedding = json.loads(pipe.readline())
sys.stderr.write("\n")
else:
embedding = find_embedding(edges, alt_hw_adj, verbose=0)
ec.write(embedding)
if len(embedding) > 0:
# Success!
break
# Continued failure -- increase edgex or edgey and try again.
if edgex < edgey:
edgex += 1
else:
edgey += 1
if not (edgex <= M and edgey <= N):
qmasm.abend("Failed to embed the problem")
logical.embedding = embedding
continue
name_list = string.join(sorted(canon2syms[i]))
sys.stderr.write(" q%-8d %s\n" % (i + 1, name_list))
sys.stderr.write("\n")
# Establish a connection to the D-Wave, and use this to talk to a solver. We
# rely on the qOp infrastructure to set the environment variables properly.
qmasm.connect_to_dwave()
# Output most or all solver properties.
if cl_args.verbose >= 1:
# Determine the width of the widest key.
max_key_len = len("Parameter")
ext_solver_properties = {}
try:
L, M, N = qmasm.chimera_topology(qmasm.solver)
ext_solver_properties["chimera_toplogy_M_N_L"] = [M, N, L]
except KeyError:
pass
ext_solver_properties.update(qmasm.solver.properties)
solver_props = ext_solver_properties.keys()
solver_props.sort()
for k in solver_props:
max_key_len = max(max_key_len, len(k))
# Output either "short" values (if verbose = 1) or all values (if
# verbose > 1).
short_value_len = 70 - max_key_len
sys.stderr.write("Encountered the following solver properties:\n\n")
sys.stderr.write(" %-*s Value\n" % (max_key_len, "Parameter"))
sys.stderr.write(" %s -----\n" % ("-" * max_key_len))
def find_dwave_embedding(logical, optimize, verbosity):
"""Find an embedding of a logical problem in the D-Wave's physical topology.
Store the embedding within the Problem object."""
# SAPI tends to choke when embed_problem is told to embed a problem
# containing a zero-weight node whose adjacent couplers all have zero
# strength. (Tested with SAPI 2.4.) To help out SAPI, we simply remove
# all zero-strength couplers.
edges = [e for e in list(logical.strengths.keys()) if logical.strengths[e] != 0.0]
edges.sort()
logical.edges = edges
try:
hw_adj = get_hardware_adjacency(qmasm.solver)
except KeyError:
# The Ising heuristic solver is an example of a solver that lacks a
# fixed hardware representation. We therefore assert that the hardware
# is an all-to-all network that connects every node to every other node.
endpoints = set([a for a, b in edges] + [b for a, b in edges])
hw_adj = [(a, b) for a in endpoints for b in endpoints if a != b]
# Tell the user if we have any hope at all of embedding the problem.
if verbosity >= 2:
report_embeddability(edges, hw_adj)
# Determine the edges of a rectangle of cells we want to use.
L, M, N = qmasm.chimera_topology(qmasm.solver)
L2 = 2*L
ncells = (qmasm.next_sym_num + L2) // L2 # Round up the number of cells.
if optimize:
edgey = max(int(math.sqrt(ncells)), 1)
edgex = max((ncells + edgey - 1) // edgey, 1)
else:
edgey = N
edgex = M
# Announce what we're about to do.
if verbosity >= 2:
sys.stderr.write("Embedding the logical adjacency within the physical topology.\n\n")
# Repeatedly expand edgex and edgey until the embedding works.
while edgex <= M and edgey <= N:
# Retain adjacencies only within the rectangle.
alt_hw_adj = []
for q1, q2 in hw_adj:
c1 = q1//L2
if c1 % M >= edgex:
continue
if c1 // M >= edgey:
continue
c2 = q2//L2
if c2 % M >= edgex:
continue
if c2 // M >= edgey:
continue
alt_hw_adj.append((q1, q2))
alt_hw_adj = set(alt_hw_adj)
logical.hw_adj = alt_hw_adj
# See if we already have an embedding in the embedding cache.
ec = EmbeddingCache(edges, alt_hw_adj)
if verbosity >= 2:
if ec.cachedir == None:
sys.stderr.write(" No embedding cache directory was specified ($QMASMCACHE).\n")
else:
sys.stderr.write(" Using %s as the embedding cache directory ...\n" % ec.cachedir)
embedding = ec.read()
if embedding == []:
# Cache hit, but embedding had failed
if verbosity >= 2:
sys.stderr.write(" Found failed embedding %s in the embedding cache.\n\n" % ec.hash)
elif embedding != None:
# Successful cache hit!
if verbosity >= 2:
sys.stderr.write(" Found successful embedding %s in the embedding cache.\n\n" % ec.hash)
logical.embedding = embedding
return
if verbosity >= 2 and ec.cachedir != None:
sys.stderr.write(" No existing embedding found in the embedding cache.\n")
# Try to find an embedding, unless we previously determined that it had
# failed.
if embedding != []:
if verbosity >= 2:
sys.stderr.write(" Trying a %dx%d unit-cell embedding ... " % (edgex, edgey))
status_file = tempfile.NamedTemporaryFile(mode="w", delete=False)
stdout_fd = os.dup(sys.stdout.fileno())
os.dup2(status_file.fileno(), sys.stdout.fileno())
embedding = find_embedding(edges, alt_hw_adj, verbose=1)
sys.stdout.flush()
os.dup2(stdout_fd, sys.stdout.fileno())
status_file.close()
if len(embedding) > 0:
sys.stderr.write("succeeded\n\n")
else:
sys.stderr.write("failed\n\n")
with open(status_file.name, "r") as status:
for line in status:
sys.stderr.write(" %s" % line)
sys.stderr.write("\n")
os.remove(status_file.name)
else:
embedding = find_embedding(edges, alt_hw_adj, verbose=0)
ec.write(embedding)
if len(embedding) > 0:
# Success!
break
# Continued failure -- increase edgex or edgey and try again.
if edgex < edgey:
edgex += 1
else:
edgey += 1
if not(edgex <= M and edgey <= N):
qmasm.abend("Failed to embed the problem")
logical.embedding = embedding
def output_bqpjson(outfile, as_qubo, problem):
"Output weights and strengths in bqpjson format, either Ising or QUBO."
# Prepare the "easy" fields.
bqp = {}
bqp["version"] = "1.0.0"
bqp["id"] = random.randint(2**20, 2**60)
bqp["scale"] = 1.0
bqp["offset"] = 0.0
if as_qubo:
bqp["variable_domain"] = "boolean"
else:
bqp["variable_domain"] = "spin"
# Prepare the list of all variables.
var_ids = set(problem.weights.keys())
for q1, q2 in problem.strengths.keys():
var_ids.add(q1)
var_ids.add(q2)
bqp["variable_ids"] = sorted(var_ids)
# Prepare the linear terms.
lin_terms = []
for q, wt in sorted(problem.weights.items()):
lin_terms.append({
"id": q,
"coeff": wt})
bqp["linear_terms"] = lin_terms
# Prepare the quadratic terms.
quad_terms = []
strengths = qmasm.canonicalize_strengths(problem.strengths)
for (q1, q2), wt in sorted(strengths.items()):
quad_terms.append({
"id_tail": q1,
"id_head": q2,
"coeff": wt})
bqp["quadratic_terms"] = quad_terms
# Prepare some metadata.
metadata = {}
if as_qubo:
metadata["description"] = "QUBO problem compiled by QMASM (https://github.com/lanl/qmasm)"
else:
metadata["description"] = "Ising problem compiled by QMASM (https://github.com/lanl/qmasm)"
metadata["command_line"] = qmasm.get_command_line()
metadata["generated"] = datetime.datetime.utcnow().isoformat()
if hasattr(problem, "embedding"):
# Physical problem
def attempt_assign(key, func):
"Try assigning a key, but don't complain if we can't."
try:
metadata[key] = func()
except KeyError:
pass
attempt_assign("dw_url", lambda: os.environ["DW_INTERNAL__HTTPLINK"])
attempt_assign("dw_solver_name", lambda: qmasm.solver_name)
props = qmasm.solver.properties
attempt_assign("dw_chip_id", lambda: props["chip_id"])
L, M, N = qmasm.chimera_topology(qmasm.solver)
metadata["chimera_cell_size"] = L*2
metadata["chimera_degree"] = max(M, N)
metadata["equivalent_ids"] = sorted(problem.chains)
metadata["variable_names"] = {s: problem.embedding[n]
for s, n in qmasm.sym_map.symbol_number_items()}
else:
metadata["variable_names"] = {s: [n]
for s, n in qmasm.sym_map.symbol_number_items()}
bqp["metadata"] = metadata
# Output the problem in JSON format.
outfile.write(json.dumps(bqp, indent=2, sort_keys=True) + "\n")
if len(discon_syms) > 0:
qmasm.abend("Disconnected variables encountered: %s" % " ".join(sorted(discon_syms)))
# Convert user-specified chains, anti-chains, and pins to assertions.
logical_ising.append_assertions_from_statements()
# Establish a connection to the D-Wave, and use this to talk to a solver. We
# rely on the qOp infrastructure to set the environment variables properly.
qmasm.connect_to_dwave()
# Output either short or all solver properties.
if cl_args.verbose >= 1:
# Introduce a few extra solver properties.
ext_solver_properties = {}
try:
L, M, N = qmasm.chimera_topology(qmasm.solver)
ext_solver_properties["chimera_toplogy_M_N_L"] = [M, N, L]
except KeyError:
pass
except qmasm.NonChimera:
pass
ext_solver_properties["solver_name"] = qmasm.solver_name
try:
ext_solver_properties["connection_name"] = os.environ["DW_INTERNAL__CONNECTION"]
except KeyError:
pass
for what in ["couplers", "qubits"]:
try:
ext_solver_properties["num_active_" + what] = len(qmasm.solver.properties[what])
except KeyError:
pass
def find_dwave_embedding(logical, optimization, verbosity, hw_adj_file):
"""Find an embedding of a logical problem in the D-Wave's physical topology.
Store the embedding within the Problem object."""
# SAPI tends to choke when embed_problem is told to embed a problem
# containing a zero-weight node whose adjacent couplers all have zero
# strength. (Tested with SAPI 2.4.) To help out SAPI, we simply remove
# all zero-strength couplers.
edges = [e for e in logical.strengths.keys() if logical.strengths[e] != 0.0]
edges.sort()
logical.edges = edges
if hw_adj_file == None:
try:
hw_adj = get_hardware_adjacency(qmasm.solver)
except KeyError:
# The Ising heuristic solver is an example of a solver that lacks a
# fixed hardware representation. We therefore assert that the
# hardware is an all-to-all network that connects every node to
# every other node.
endpoints = set([a for a, b in edges] + [b for a, b in edges])
hw_adj = [(a, b) for a in endpoints for b in endpoints if a != b]
else:
hw_adj = read_hardware_adjacency(hw_adj_file, verbosity)
# Tell the user if we have any hope at all of embedding the problem.
if verbosity >= 2:
report_embeddability(edges, hw_adj)
# Determine the edges of a rectangle of cells we want to use. If we read
# the topology from a file or otherwise can't prove that we have a Chimera
# graph, we call this rectangle 0x0 and force the main embedding loop to
# exit after a single iteration because we don't know the topology is even
# rectangular.
edgex = 0
edgey = 0
M = 0
N = 0
num_vars = len(qmasm.sym_map.all_numbers())
try:
if hw_adj_file == None:
L, M, N = qmasm.chimera_topology(qmasm.solver)
L2 = 2*L
ncells = (num_vars + L2) // L2 # Round up the number of cells.
if optimization >= 2:
edgey = max(int(math.sqrt(ncells)), 1)
edgex = max((ncells + edgey - 1) // edgey, 1)
else:
edgey = N
edgex = M
except qmasm.NonChimera:
pass
# Announce what we're about to do.
if verbosity >= 2:
sys.stderr.write("Embedding the logical adjacency within the physical topology.\n\n")
# Repeatedly expand edgex and edgey until the embedding works.
while edgex <= M and edgey <= N:
if edgex == M and edgey == N:
alt_hw_adj = hw_adj
else:
# Retain adjacencies only within the rectangle.
alt_hw_adj = []
for q1, q2 in hw_adj:
c1 = q1//L2
if c1 % M >= edgex:
continue
if c1 // M >= edgey:
continue
c2 = q2//L2
if c2 % M >= edgex:
continue
if c2 // M >= edgey:
continue
alt_hw_adj.append((q1, q2))
alt_hw_adj = set(alt_hw_adj)
logical.hw_adj = alt_hw_adj
# See if we already have an embedding in the embedding cache.
ec = EmbeddingCache(edges, alt_hw_adj)
if verbosity >= 2:
if ec.cachedir == None:
sys.stderr.write(" No embedding cache directory was specified ($QMASMCACHE).\n")
else:
sys.stderr.write(" Using %s as the embedding cache directory ...\n" % ec.cachedir)
embedding = ec.read()
if embedding == []:
# Cache hit, but embedding had failed
if verbosity >= 2:
sys.stderr.write(" Found failed embedding %s in the embedding cache.\n\n" % ec.hash)
elif embedding != None:
# Successful cache hit!
if verbosity >= 2:
sys.stderr.write(" Found successful embedding %s in the embedding cache.\n\n" % ec.hash)
logical.embedding = embedding
return
if verbosity >= 2 and ec.cachedir != None:
sys.stderr.write(" No existing embedding found in the embedding cache.\n")
# Try to find an embedding, unless we previously determined that it had
# failed.
if embedding != []:
if verbosity >= 2:
# SAPI's find_embedding is hard-wired to write to stdout.
# Trick it into writing into a pipe instead.
if edgex == 0 and edgey == 0:
sys.stderr.write(" Trying to embed ... ")
else:
sys.stderr.write(" Trying a %dx%d unit-cell embedding ...\n\n" % (edgex, edgey))
sepLine = "=== EMBEDDING ===\n"
r, w = os.pipe()
pid = os.fork()
if pid == 0:
# Child -- perform the embedding.
os.close(r)
os.dup2(w, sys.stdout.fileno())
embedding = find_embedding(edges, alt_hw_adj, verbose=1)
sys.stdout.flush()
os.write(w, sepLine)
os.write(w, json.dumps(embedding) + "\n")
os.close(w)
os._exit(0)
else:
# Parent -- report the embedding's progress.
os.close(w)
pipe = os.fdopen(r, "r", 10000)
while True:
try:
rstr = pipe.readline()
if rstr == sepLine:
break
if rstr == "":
qmasm.abend("Embedder failed to terminate properly")
sys.stderr.write(" %s" % rstr)
except:
pass
# Receive the embedding from the child.
embedding = json.loads(pipe.readline())
sys.stderr.write("\n")
else:
embedding = find_embedding(edges, alt_hw_adj, verbose=0)
ec.write(embedding)
if len(embedding) > 0:
# Success!
break
# Continued failure -- increase edgex or edgey and try again.
if edgex < edgey:
edgex += 1
else:
edgey += 1
if not(edgex <= M and edgey <= N):
qmasm.abend("Failed to embed the problem")
logical.embedding = embedding
