def match_planar_3D(lattice_size,stabilizer_type,anyon_positions,time_space_weights,boundary_weight = 1.11 ,special_weights=[1,1,1],print_graph=False):
## specify matching parameters
max_time_separation = 15
[wS,wT]=time_space_weights
wB = wS if boundary_weight == 1.11 else boundary_weight
[w1,w2,w3]=special_weights
total_time=len(anyon_positions)
nodes_list=[item for sublist in anyon_positions for item in sublist]
n_nodes=len(nodes_list)
if n_nodes==0:
return []
node_index=[]
count=0
for x in anyon_positions:
node_index+=[[count+i for i in range(len(x))]]
count+=len(x)
b_node_index=[[index+n_nodes for index in t] for t in node_index]
all_boundary_nodes=[]
all_boundary_nodes2=[]
## LOOKUP TABLES
m = 2*lattice_size +1
weight_lookup={}
for p in range(-1,m+1):
weight_lookup[p]={}
for q in range(-1,m+1):
weight_lookup[p][q]=abs(p-q)
nodes1 = []
nodes2 = []
weights = []
## PART 1: Complete 2 copies of the graph between all real nodes
for i in range(n_nodes -1):
(pt,p0,p1)=nodes_list[i]
for j in range(i+1,n_nodes):
(qt,q0,q1)=nodes_list[j]
wt=(qt-pt)
if wt>=max_time_separation: break
wx = weight_lookup[q0][p0]
wy = weight_lookup[q1][p1]
weight = (wS*(wx+wy)+wt*wT)
if (wt,wx,wy) in [(1,2,0),(1,0,2)]:
weight *= w1
elif (wt,wx,wy) == (1,0,0):
weight *= w2
elif (wt,wx,wy) in [(0,2,0),(0,0,2)]:
weight *=w3
#weight = weight_lookup[q0][p0]+weight_lookup[q1][p1]+wt*wT
nodes1 +=[i,i+n_nodes]
nodes2 +=[j,j+n_nodes]
weights+=[weight,weight]
## PART 2: Link each node to its equivalent in the second graph
boundary_nodes_list=[]
for i in range(n_nodes):
(pt,p0,p1)=nodes_list[i]
if stabilizer_type =="star":
(bt,b0,b1)=(pt,p0,-1 if p1<lattice_size else m)
elif stabilizer_type=="plaquette":
(bt,b0,b1)=(pt,-1 if p0<lattice_size else m,p1)
else:
print "stabilizer_type must be either *star* or *plaquette*"
sys.exit(0)
boundary_nodes_list+=[(bt,b0,b1)]
weight = weight_lookup[p0][b0]+weight_lookup[p1][b1]
nodes1+=[i]
nodes2+=[i+n_nodes]
weights+=[int(weight*wB/wS)]
if print_graph==True:
print zip(nodes1,nodes2,weights)
# print 't0 = ', t0
# print 't1 = ', time.time()-tt1
# print 't2 = ', t22
# print 't3 = ', t3
n_edges=len(nodes1)
################ MATCHING ###################
#tt4 = time.time()
# matching=pm.getMatching(2*n_nodes,graphArray)
matching = pm.getMatching_fast(2*n_nodes,nodes1,nodes2,weights)
# print 'matching ', time.time()-tt4
#############################################
if print_graph==True:
print "Matching"
print matching
matching_pairs=[[i,matching[i]] for i in range(2*n_nodes) if matching[i]>i]
all_positions=nodes_list+boundary_nodes_list
points=[] if len(matching_pairs)==0 else [[all_positions[i] for i in x] for x in matching_pairs]
return points
def match_planar_3D(lattice_size,
stabilizer_type,
anyon_positions,
time_space_weights=[1, 1],
boundary_weight=-1,
print_graph=False):
""" Finds a matching to fix the errors in a 3D planar code given the positions of '-1' stabilizer outcomes
Parameters:
-----------
lattice_size -- The dimension of the code
stabilizer_type -- defines the stabilizer basis, can take the value "star" or "plaquette"
anyon_positions -- A list of the locations of all '-1' value stabilizers in the 3D parity lattice. [[x0,y0,t0],[x1,y1,t1],...]
time_space_weights -- The multiplicative weighting that should be assigned to graph edges in the [space,time] dimensions. Default: [1,1]
boundary_weight -- multiplicative weight to be assigned to edges matching to the boundary. if no boundary_weight specified, set boundary_weight = space_weight
print_graph -- Set to True to print the constructed graph. Default: False.
Returns:
--------
A list containing all the input anyon positions grouped into pairs. [[[x0,y0,t0],[x1,y1,t1]],[[x2,y2,t2],...
"""
max_time_separation = 15 # This determines the maximum time separation of edges that are added to the graph
[wS, wT] = time_space_weights
wB = wS if boundary_weight == -1 else boundary_weight #if boundary weight not specifiedm, let wB=wS
total_time = len(anyon_positions)
nodes_list = [item for sublist in anyon_positions for item in sublist]
n_nodes = len(nodes_list)
# exclude edge case where no anyons exist.
if n_nodes == 0:
return []
node_index = []
count = 0
for x in anyon_positions:
node_index += [[count + i for i in range(len(x))]]
count += len(x)
b_node_index = [[index + n_nodes for index in t] for t in node_index]
all_boundary_nodes = []
all_boundary_nodes2 = []
## LOOKUP TABLES
m = 2 * lattice_size + 1
weight_lookup = {}
for p in range(-1, m + 1):
weight_lookup[p] = {}
for q in range(-1, m + 1):
weight_lookup[p][q] = wS * abs(p - q)
## CONSTRUCT GRAPH
## create a graph containing all possible matchings between pairs of anyons (given constraints)
## This is represented as three lists:
nodes1 = []
nodes2 = []
weights = []
## PART 1: Complete graph between all real nodes
for i in range(n_nodes - 1):
(pt, p0, p1) = nodes_list[i]
for j in range(i + 1, n_nodes):
(qt, q0, q1) = nodes_list[j]
wt = (qt - pt)
if wt >= max_time_separation: break
weight = weight_lookup[q0][p0] + weight_lookup[q1][p1] + wt * wT
nodes1 += [i]
nodes2 += [j]
weights += [weight]
## PART 2: Generate list of boundary nodes linked to each real node
boundary_nodes_list = []
for i in range(n_nodes):
(pt, p0, p1) = nodes_list[i]
if stabilizer_type == "star":
(bt, b0, b1) = (pt, p0, -1 if p1 < lattice_size else m)
elif stabilizer_type == "plaquette":
(bt, b0, b1) = (pt, -1 if p0 < lattice_size else m, p1)
else:
print "stabilizer_type must be either *star* or *plaquette*"
sys.exit(0)
weight = weight_lookup[p0][b0] + weight_lookup[p1][b1]
nodes1 += [i]
nodes2 += [i + n_nodes]
weights += [int(weight * wB / wS)]
boundary_nodes_list += [(bt, b0, b1)]
## PART 3: Complete graph between all boundary nodes
for i in range(n_nodes - 1):
(pt, p0, p1) = boundary_nodes_list[i]
for j in range(i + 1, n_nodes):
(qt, q0, q1) = boundary_nodes_list[j]
wt = (qt - pt)
if wt >= 5: break
nodes1 += [n_nodes + i]
nodes2 += [n_nodes + j]
weights += [0]
if print_graph == True:
print zip(nodes1, nodes2, weights)
n_edges = len(nodes1)
## MAKE MATCHING.
## Call the blossom5 perfect matching algorithm to return a matching.
## The form of the returned variable <matching> is a list of pairs of node numbers.
matching = pm.getMatching_fast(2 * n_nodes, nodes1, nodes2, weights)
if print_graph == True:
print "Matching"
print matching
## REFORMAT MATCHING PAIRS
## Take <matching> and turn it into a list of paired anyon positions.
matching_pairs = [[i, matching[i]] for i in range(2 * n_nodes)
if matching[i] > i]
all_positions = nodes_list + boundary_nodes_list
points = [] if len(matching_pairs) == 0 else [
[all_positions[i] for i in x] for x in matching_pairs
]
return points
def match_planar_3D(lattice_size,stabilizer_type,anyon_positions,time_space_weights,boundary_weight = 1,print_graph=False):
max_time_separation = 15
t00 = time.time()
total_time=len(anyon_positions)
nodes_list=[item for sublist in anyon_positions for item in sublist]
n_nodes=len(nodes_list)
[wS,wT]=time_space_weights
wB = wS if boundary_weight == 1 else boundary_weight
if n_nodes==0:
return []
node_index=[]
count=0
for x in anyon_positions:
node_index+=[[count+i for i in range(len(x))]]
count+=len(x)
b_node_index=[[index+n_nodes for index in t] for t in node_index]
all_boundary_nodes=[]
boundary_node=None
## LOOKUP TABLES
m = 2*lattice_size +1
weight_lookup={}
for p in range(-1,m+1):
weight_lookup[p]={}
for q in range(-1,m+1):
weight_lookup[p][q]=wS*abs(p-q)
#------------------------------------------------------------
nodes1 = []
nodes2 = []
weights = []
## PART 1: Complete graph between all real nodes
for i in range(n_nodes -1):
(pt,p0,p1)=nodes_list[i]
for j in range(i+1,n_nodes):
(qt,q0,q1)=nodes_list[j]
wt=(qt-pt)
if wt>=max_time_separation: break
weight = weight_lookup[q0][p0]+weight_lookup[q1][p1]+wt*wT
nodes1 +=[i]
nodes2 +=[j]
weights+=[weight]
#-------------------------------------
## PART 2: Create boundary node for each
for t in range(total_time):
n_list_t=anyon_positions[t]
n_nodes_t=len(n_list_t)
n_index_t=node_index[t]
b_index_t=b_node_index[t]
n_nodes_t_minus1 = n_nodes_t - 1
# for every node, create a boundary node and joining edge
boundary_node_positions_t=[]
if stabilizer_type == "star":
for i in range(n_nodes_t):
(pt,p0,p1)=n_list_t[i]
(bt,b0,b1)=(t,p0,-1 if p1<lattice_size else m)
boundary_node_positions_t+=[[bt,b0,b1]]
#weight=sW*(abs(p0-b0)+abs(p1-b1))
weight = weight_lookup[p0][b0]+weight_lookup[p1][b1]
nodes1+=[n_index_t[i]]
nodes2+=[b_index_t[i]]
weights+=[int(weight*wB/wS)]
if i==0:
if isinstance(boundary_node,int):
boundary_node_update=b_index_t[0]
nodes1+=[boundary_node_update]
nodes2+=[boundary_node]
weights+=[0]
boundary_node=copy.copy(boundary_node_update)
else:
boundary_node=copy.copy(b_index_t[0])
elif stabilizer_type=="plaquette":
for i in range(n_nodes_t):
(pt,p0,p1)=n_list_t[i]
(bt,b0,b1)=(t,-1 if p0<lattice_size else m,p1)
boundary_node_positions_t+=[[bt,b0,b1]]
weight = weight_lookup[p0][b0]+weight_lookup[p1][b1]
# graphArray+=[[n_index_t[i],b_index_t[i],weight]]
nodes1+=[n_index_t[i]]
nodes2+=[b_index_t[i]]
weights+=[int(weight*wB/wS)]
if i==0:
if isinstance(boundary_node,int):
boundary_node_update=b_index_t[0]
# graphArray+=[[boundary_node_update,boundary_node,0]]
nodes1+=[boundary_node_update]
nodes2+=[boundary_node]
weights+=[0]
boundary_node=copy.copy(boundary_node_update)
else:
boundary_node=copy.copy(b_index_t[0])
else:
print "stabilizer_type must be either **star** or **plaquette**"
return 0
## save one boundary node to connect to other layers
all_boundary_nodes+=boundary_node_positions_t
#boundary_nodes_positions_t=
#[[pt,p0,-1 if p1<lattice_size else 2*lattice_size+1] for [pt,p0,p1] in node_list_t]
#if stabilizer_type=="star" else [[pt,-1 if p0<lattice_size else 2*lattice_size,p1]]
tt2 = time.time()
# fully connect boundary nodes with weight 0
for i in range(n_nodes_t-1):
# for j in range(n_nodes_t-i-1):
for j in range(i+1,n_nodes_t):
# graphArray+=[[b_index_t[i],b_index_t[i+j+1],0]]
nodes1+=[b_index_t[i]]
#nodes2+=[b_index_t[i+j+1]]
nodes2+=[b_index_t[j]]
weights+=[0]
# t22 += time.time()-tt2
if print_graph==True:
print zip(nodes1,nodes2,weights)
# print 't0 = ', t0
# print 't1 = ', time.time()-tt1
# print 't2 = ', t22
# print 't3 = ', t3
n_edges=len(nodes1)
################ MATCHING ###################
#tt4 = time.time()
# matching=pm.getMatching(2*n_nodes,graphArray)
matching = pm.getMatching_fast(2*n_nodes,nodes1,nodes2,weights)
# print 'matching ', time.time()-tt4
#############################################
if print_graph==True:
print "Matching"
print matching
matching_pairs=[[i,matching[i]] for i in range(2*n_nodes) if matching[i]>i]
all_positions=nodes_list+all_boundary_nodes
points=[] if len(matching_pairs)==0 else [[all_positions[i] for i in x] for x in matching_pairs]
return points
def match_planar_3D(lattice_size,stabilizer_type,anyon_positions,time_space_weights=[1,1],boundary_weight = -1 ,print_graph=False):
""" Finds a matching to fix the errors in a 3D planar code given the positions of '-1' stabilizer outcomes
Parameters:
-----------
lattice_size -- The dimension of the code
stabilizer_type -- defines the stabilizer basis, can take the value "star" or "plaquette"
anyon_positions -- A list of the locations of all '-1' value stabilizers in the 3D parity lattice. [[x0,y0,t0],[x1,y1,t1],...]
time_space_weights -- The multiplicative weighting that should be assigned to graph edges in the [space,time] dimensions. Default: [1,1]
boundary_weight -- multiplicative weight to be assigned to edges matching to the boundary. if no boundary_weight specified, set boundary_weight = space_weight
print_graph -- Set to True to print the constructed graph. Default: False.
Returns:
--------
A list containing all the input anyon positions grouped into pairs. [[[x0,y0,t0],[x1,y1,t1]],[[x2,y2,t2],...
"""
max_time_separation = 15 # This determines the maximum time separation of edges that are added to the graph
[wS,wT]=time_space_weights
wB = wS if boundary_weight == -1 else boundary_weight #if boundary weight not specifiedm, let wB=wS
total_time=len(anyon_positions)
nodes_list=[item for sublist in anyon_positions for item in sublist]
n_nodes=len(nodes_list)
# exclude edge case where no anyons exist.
if n_nodes==0:
return []
node_index=[]
count=0
for x in anyon_positions:
node_index+=[[count+i for i in range(len(x))]]
count+=len(x)
b_node_index=[[index+n_nodes for index in t] for t in node_index]
all_boundary_nodes=[]
all_boundary_nodes2=[]
## LOOKUP TABLES
m = 2*lattice_size +1
weight_lookup={}
for p in range(-1,m+1):
weight_lookup[p]={}
for q in range(-1,m+1):
weight_lookup[p][q]=wS*abs(p-q)
## CONSTRUCT GRAPH
## create a graph containing all possible matchings between pairs of anyons (given constraints)
## This is represented as three lists:
nodes1 = []
nodes2 = []
weights = []
## PART 1: Complete graph between all real nodes
for i in range(n_nodes -1):
(pt,p0,p1)=nodes_list[i]
for j in range(i+1,n_nodes):
(qt,q0,q1)=nodes_list[j]
wt=(qt-pt)
if wt>=max_time_separation: break
weight = weight_lookup[q0][p0]+weight_lookup[q1][p1]+wt*wT
nodes1 +=[i]
nodes2 +=[j]
weights+=[weight]
## PART 2: Generate list of boundary nodes linked to each real node
boundary_nodes_list = []
for i in range(n_nodes):
(pt,p0,p1)=nodes_list[i]
if stabilizer_type =="star":
(bt,b0,b1)=(pt,p0,-1 if p1<lattice_size else m)
elif stabilizer_type=="plaquette":
(bt,b0,b1)=(pt,-1 if p0<lattice_size else m,p1)
else:
print "stabilizer_type must be either *star* or *plaquette*"
sys.exit(0)
weight = weight_lookup[p0][b0]+weight_lookup[p1][b1]
nodes1+=[i]
nodes2+=[i+n_nodes]
weights+=[int(weight*wB/wS)]
boundary_nodes_list+=[(bt,b0,b1)]
## PART 3: Complete graph between all boundary nodes
for i in range(n_nodes -1):
(pt,p0,p1)=boundary_nodes_list[i]
for j in range(i+1,n_nodes):
(qt,q0,q1)=boundary_nodes_list[j]
wt=(qt-pt)
if wt>=5: break
nodes1 +=[n_nodes+i]
nodes2 +=[n_nodes+j]
weights+=[0]
if print_graph==True:
print zip(nodes1,nodes2,weights)
n_edges=len(nodes1)
## MAKE MATCHING.
## Call the blossom5 perfect matching algorithm to return a matching.
## The form of the returned variable <matching> is a list of pairs of node numbers.
matching = pm.getMatching_fast(2*n_nodes,nodes1,nodes2,weights)
if print_graph==True:
print "Matching"
print matching
## REFORMAT MATCHING PAIRS
## Take <matching> and turn it into a list of paired anyon positions.
matching_pairs=[[i,matching[i]] for i in range(2*n_nodes) if matching[i]>i]
all_positions=nodes_list+boundary_nodes_list
points=[] if len(matching_pairs)==0 else [[all_positions[i] for i in x] for x in matching_pairs]
return points
