Wolfram/TensorNetworks | Paclet Repository

Wolfram`TensorNetworks`

RandomTensorNetwork

RandomTensorNetwork [{n,m},maxDim]
	creates a random tensor network with graph RandomGraph[{n,m}] and bond dimensions up to maxDim .

RandomTensorNetwork [graph,maxDim]
	uses an arbitrary graph and samples each bond dimension from {2,maxDim} .

RandomTensorNetwork [graph,{dim}]
	makes every bond dimension exactly dim .

RandomTensorNetwork [graph,dim,r]
	adds up to r free legs per vertex on top of its degree.

RandomTensorNetwork ["MPS"[n,χ,d]]
	creates a random Matrix Product State of length n , bond dimension χ and physical dimension d .

RandomTensorNetwork ["TT"[n,χ]]
	creates a Tensor Train of length n and bond dimension χ (no physical legs).

RandomTensorNetwork ["MPO"[n,χ,d]]
	creates a random Matrix Product Operator of length n with bond dimension χ and physical dimension d .

RandomTensorNetwork ["PEPS"[{rows,cols},χ,d]]
	creates a Projected Entangled Pair State on a rows×cols grid.

RandomTensorNetwork ["TTN"[depth,χ,b]]
	creates a Tree Tensor Network of binary depth depth with branching factor b .

RandomTensorNetwork ["MERA"[w,χ,L]]
	creates a Multi-scale Entanglement Renormalization Ansatz of width w and L coarse-graining layers.

Details and Options

▪

The result of

RandomTensorNetwork

is a

TensorNetwork

object; all its property accessors apply (

"Tensors"

"Hyperedges"

"FreeIndices"

"Bonds"

, …).

▪

For the general graph form, the rank of each vertex is sampled uniformly from

{VertexDegree[v],VertexDegree[v]+r}

; the extra legs are free indices of the resulting network.

▪

Free leg dimensions match bond dimensions: with the

{dim}

form every index has dimension

dim

; with the

maxDim

form every index dimension is an independent random integer in

{2,maxDim}

▪

For named topologies the indices are integer labels assigned in a fixed, predictable layout. For an MPS of length

, bond indices use

1,…,n-1

and physical indices use

n+1,…,2n

▪

For an MPO of length

, physical input indices start at

n+1

and physical output indices at

2n+1

; this leaves the bulk bond labels

1,…,n-1

untouched.

▪

The scalar-arguments form

"PEPS"[rows,cols,χ,d]

is equivalent to the list-arguments form

"PEPS"[{rows,cols},χ,d]

▪

Tensor entries are independent draws from a uniform distribution on

{-1,1}

(real) or on a complex square of side

centered at the origin (

"Complex"

). The state is not normalized.

▪

The following options can be given:

	Method	Automatic	use real (default) or complex random tensors
	"Boundary"	"Open"	for chain topologies (MPS, TT, MPO), choose "Open" or "Periodic"

Examples

(21)

Basic Examples

(4)

Create a random tensor network from a small random graph:

In[1]:=

RandomTensorNetwork

[{5,8},3]

Out[1]=

TensorNetwork

Tensors: 5	Binary: Yes
Free indices: 4	Sparse: No
Output dimension: 16



Create a random Matrix Product State of length 4 with bond dimension 2:

In[1]:=

RandomTensorNetwork

["MPS"[4,2,2]]

Out[1]=

TensorNetwork

Tensors: 4	Binary: Yes
Free indices: 4	Sparse: No
Output dimension: 16



Use periodic boundary conditions to get a uniform ring of rank-3 tensors:

In[1]:=

RandomTensorNetwork

["MPS"[4,2,2],"Boundary""Periodic"]

Out[1]=

TensorNetwork

Tensors: 4	Binary: Yes
Free indices: 4	Sparse: No
Output dimension: 16



Properties of the generated network can be queried directly:

In[1]:=

RandomTensorNetwork

["MPS"[4,2,2]]["Hyperedges"]

Out[1]=

{{1,5},{1,2,6},{2,3,7},{3,8}}

Scope

(11)



Options

(3)



Applications

(2)



Properties & Relations

(1)



SeeAlso

TensorNetwork

▪

TensorNetworkQ

▪

BinaryTensorNetwork

▪

TensorNetworkContract

▪

OptimalContractionPath

▪

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▪

▪

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TechNotes

▪

Building Tensor Networks

▪

MPS Algorithms

RelatedGuides

▪

TensorNetworks

RelatedLinks

▪

Tensor Network on Wikipedia