# Questions tagged [tensor-network]

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### Number of operations in tensor networks [closed]

I cannot understand how the number of operations in these Tensor Networks differ and are $D^4$ and $D^5$. I'd appreciate any help. source: https://arxiv.org/abs/1306.2164
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### How to left-normalize a Matrix Product State

If you are reading this, you should probably have some background in Tensor Networks or Matrix Products States or this will be insufficient information. So when putting a MPS into left (or right) ...
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### Is there any relation between density matrix renormalization group (DMRG) and renormalization group (RG)?

Probably I am going to receive many down-votes for this post but I really need to ask this question here. I am new to statistical mechanics. I wanted to learn Density Matrix Renormalization Group (...
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### Resource recommendation: Tensor Networks

I want to learn tensor network methods for condensed matter systems. I went through some basic papers (i.e. 1,2) and come to know that there are many things (i.e. different math, tensors, ...
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### Left and Right Eigenvectors of Transfer Matrix in Matrix Product States (MPS)

Let $$\lvert{\psi}\rangle=\sum_{i_1i_2...i_n}Tr(A^{}_{i_1}A^{}_{i_2}...A^{[n]}_{i_n})\lvert{i_1 i_2...i_n}\rangle$$ be a MPS, where $i_k=1,2...d$ and $A^{[k]}_{i_k}$ are $D\times D$ matrices ...
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### The physical picture of uncle Hamiltonian?

Uncle Hamiltonian was built to show the complex relationship between MPS (Matrix Product State) states and Hamiltonians, which claims that for a block injective MPS state, we can build a local ...
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### Constructing PEPS representation of an arbitrary quantum state

Given a quantum state we can construct its MPS (Matrix Product State) representation by doing a series of singular value decompositions. Given the freedom to choose arbitrary bond dimensions the MPS ...
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### Tensor Network from Lattice

I read an article about tensor networks and they seem very interesting and a promising approach to studying the relations between entanglement, gravity and quantum information. How does this network ...
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### If a state can be efficiently represented by a Projected Entangled Pair State (PEPS), can we prepare it physically?

If we can use PEPS (Projected Entangled Pair State) to represent a many body quantum state, can we generate it by a quantum computer? As far as I can understand, PEPS is dual to a quantum computer ...
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### What is some good reference for tensor network?

I am a physicist who is now doing some research in quantum information, which might involve tensor network.
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### How to code Tensor Networks?

I'm interested in learning tensor networks, I've been reading some introductory articles about this. The problem is that these articles mostly discuss the theoretical definitions for tensor networks ...
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### What's the tensor network representation for local ground state?

It's well known that many topological phases can be represented using matrix product state and PEPS. Example, toric code, $H=-\sum_{v}A_v-\sum_p B_p$. My question is: What's the tensor network ...
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### Relationship between the 'relevant states' and the states that can be generated by a quantum computer?

In the huge quantum state space, for example n-qubit space has a state number as $2^{2^n}$, usually we are interested in two different kinds of 'physical' states. Set 1: The relevant state which is ...
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### Dependence of tensor network on underlying physical lattice structure

I have noticed that the majority of research on tensor networks has focused on lattice systems. For example, in this review, the author mentions using PEPS on different lattices such as triangular, ...
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### Question about general direction of development of application of Tensor Networks to AdS/CFT

I am quite interested in the area of application of Tensor Networks(TNs) to AdS/CFT correspondence. I would like to clarify certain points in order to get better general picture. What is the main ...
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### Tensor network Renormalization group

I am working on Tensor network Renormalization group. While I am trying to implement TRG on Honeycomb lattice I got stuck on pairing two three rank tensors and represent it as D^2*D^2 matrix. Can you ...
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### How to compute the MPS representation for a sequence of asymptotically gapped quantum spin chains

Suppose I have a sequence of gapped, spin-$1/2$, translationally invariant quantum spin chains $\{H_1, H_2,H_3\cdots\}$ with interactions of range $\leq 2$ (i.e. no further than nearest-neighbors). ...
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### Simple analytic examples of Multi-scale Entanglement Renormalization Ansatz (MERA)

I want to understand Multi-scale Entanglement Renormalization Ansatz (MERA) with very elementary examples. So far I could find references which are mostly based on numerics. It would be a great help ...
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### Examples of Matrix Product States

Matrix product states (MPS) are a way of representing a (many-body) wavefunction. The method has been described, for example, in The density-matrix renormalization group in the age of matrix ...
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### Is Schmidt Decomposition well defined for periodic matrix product representation(MPS)?

We are able to perform Schmidt decomposition for open-boundary MPSs with dimension of boundary bond $m_0 = 1$, $|\psi\rangle=\sum w_{a_l}|a_l\rangle_L|a_l\rangle_R$. Because we can make \$|a_l\rangle_{...
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### Exponential decay of correlation in PEPS

PEPS (Projected Entangled Pair State) is a tensor network that plays the same role in two dimensional lattice as MPS (Matrix Product State) plays in one dimensional spin chain. A good introduction can ...
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### Difference between DMRG (density matrix renomalization group) and MPS (matrix product states)?

I am learning DMRG recently. I noticed there are many papers both in the DMRG approach and MPS (such as variational matrix product state (VMPS) by F.Verstraete and J.I.Cirac) approach. In my eyes, ...