Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`
BinaryTensorNetwork  |
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When [] is , the input network is already binary and returns it unchanged.
tn
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Each hyperedge – an index shared by tensors – is replaced by a fresh rank- (a copy tensor) that joins the original tensors through new bond indices, leaving every index in the result shared by at most two tensors.
i
k≥3
k
k
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The third slot of – the output index list [] – is forwarded unchanged to the binary network.
tn
"Output"
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Path-finders and require a binary network. applies internally on hyperedge inputs; call it directly when feeding a network to a path-finder.
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The binarized network contracts to the same tensor as the original, since each inserted spider equals a multidimensional .
Examples
(9)
Basic Examples
(2)
Build a three-tensor network in which the index i2 is shared by all three tensors, so the network is not binary:
In[1]:=
tensors=RandomReal[{-1,1},{3,2,2,2}];
In[2]:=
tn=
[tensors,{{i1,i2,i3},{i2,i4,i5},{i2,i3,i6}}]
 | TensorNetwork |
Out[2]=
TensorNetwork
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Test if it is a binary (pairwise) tensor network:
In[3]:=
tn["BinaryQ"]
Out[3]=
False
It is clear from the hypergraph that the index i2 is shared by 3 tensors:
In[4]:=
Quiet[tn["Hypergraph"],ResourceObject::updavb]
Out[4]=
Convert to a binary tensor network. The returned object is itself a object whose summary box reports Binary: Yes:
In[5]:=
bin=
[tn]
| BinaryTensorNetwork |
Out[5]=
TensorNetwork
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After binarization the new network reports the binary property as True and has size larger than the original (one extra spider per hyperedge):
In[6]:=
bin["BinaryQ"]
Out[6]=
True
In[7]:=
 | TensorNetworkSize |
Out[7]=
3
In[8]:=
| TensorNetworkSize |
Out[8]=
4
Every standard tensor-network topology (MPS, PEPS, TTN, MERA, MPO) produced by RandomTensorNetwork is already binary. Start from an MPS of length 4:
In[1]:=
mps=BlockRandomSeedRandom[1];
["MPS"[4,2,2]]
 | RandomTensorNetwork |
Out[1]=
TensorNetwork
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In[2]:=
| BinaryTensorNetworkQ |
Out[2]=
True
In[3]:=
| BinaryTensorNetwork |
Out[3]=
TensorNetwork
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Identity is structural, not just numerical:
In[4]:=
| BinaryTensorNetwork |
Out[4]=
True
Scope
(3)
Applications
(2)
Properties & Relations
(2)
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