Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`
MPSTruncate  |
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Examples
(4)
Scope
(1)
The compressed MPS has smaller bonds. Compare the bond dictionaries before and after:
In[1]:=
mps=BlockRandomSeedRandom[42];
["MPS"[8,4,2]];mps["Bonds"]
 | RandomTensorNetwork |
Out[1]=
{{,}4,{,}4,{,}4,{,}4,{,}4,{,}4,{,}4}
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In[1]:=
mps=BlockRandomSeedRandom[42];
["MPS"[8,4,2]];compressed=
[mps,2];compressed["Bonds"]
| RandomTensorNetwork |
 | MPSTruncate |
Out[1]=
{{,}2,{,}2,{,}2,{,}2,{,}2,{,}2,{,}2}
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Truncation throws information away. The fidelity measures how much was kept:
〈original|compressed〉
original·compressed
In[2]:=
compressed=
[mps,2];mps=BlockRandomSeedRandom[42];
["MPS"[8,4,2]];fidelity=Abs
[mps,compressed]
[mps]*
[compressed]
| MPSTruncate |
| RandomTensorNetwork |
 | MPSOverlap |
| MPSNorm |
| MPSNorm |
Out[2]=
0.85481
A larger maxBond drops fewer singular values and yields higher fidelity:
In[1]:=
mps=BlockRandomSeedRandom[42];
["MPS"[8,4,2]];compressed3=
[mps,3];Abs
[mps,compressed3]
[mps]*
[compressed3]
| RandomTensorNetwork |
| MPSTruncate |
| MPSOverlap |
| MPSNorm |
| MPSNorm |
Out[1]=
0.940158
If maxBond is at least as large as every existing bond, no singular values are discarded:
In[2]:=
smallMPS=BlockRandomSeedRandom[42];
["MPS"[5,2,2]];smallMPS["Bonds"]
| RandomTensorNetwork |
Out[2]=
{{,}2,{,}2,{,}2,{,}2}
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In[1]:=
smallMPS=BlockRandomSeedRandom[42];
["MPS"[5,2,2]];
[smallMPS,4]["Bonds"]
| RandomTensorNetwork |
 | MPSTruncate |
Out[1]=
{{,}2,{,}2,{,}2,{,}2}
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Options
(1)
Applications
(1)
Properties & Relations
(1)
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Build an 8-site MPS with bond dimension 4 and physical dimension 2:
In[1]:=
mps=BlockRandomSeedRandom[42];
["MPS"[8,4,2]]
| RandomTensorNetwork |
Out[1]=
TensorNetwork
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Compress the MPS to bond dimension 2. The result is a new TensorNetwork object:
In[2]:=
compressed=
[mps,2]
| MPSTruncate |
Out[2]=
TensorNetwork
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Skip the post-truncation rescale with "Normalize" -> False:
In[3]:=
rawCompressed=
[mps,2,"Normalize"False]
| MPSTruncate |
Out[3]=
TensorNetwork
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By default the result has unit norm:
In[4]:=
 | MPSNorm |
Out[4]=
1.
Without rescaling, the norm reflects the discarded singular values:
In[5]:=
| MPSNorm |
Out[5]=
19.1745
""