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Questions tagged [tensor-networks]

A tensor network is simply a countable collection of tensors connected by contractions. ‘Tensor network methods’ is the term given to the entire collection of associated tools, which are regularly employed in modern quantum information science, condensed matter physics, mathematics and computer science. (arXiv:1708.00006)

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Categories and types of quantum inspired algorithms

I have a question concerning "quantum-inspired" algorithms. There seem to be several types of algorithms that fall into this category. Some examples are: Ewin's dequantized algorithms ...
sheesymcdeezy's user avatar
10 votes
2 answers
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What can tensor networks mean for quantum computing?

I am trying to understand what the importance of tensor networks is (or will/could be) for quantum computing. Does it make sense to study tensor networks deeply and develop them further to help pave ...
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How can blackholes be fast information scramblers?

I noticed that there was already a post discussing the fast scrambling property of black holes. But it seems no satisfactory answer was given. As mentioned by L. Susskind et. al, the fast scrambling ...
XXDD's user avatar
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Is Density Matrix simulation same as Tensor Network simulation?

I read that there are two major ways of simulating quantum circuits - State Vector Simulation and Tensor Network Simulation. But Qiskti provides a backend to simulate state-vectors and a backend for ...
Dexter Mandark's user avatar
5 votes
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How to split a 2-local unitary operator through singular value decomposition?

I’m studying the paper Expressive power of tensor-network factorizations for probabilistic modeling by Glasser et al. In equation S6 (page 2 of supplementary material, excerpt of paper figure below) ...
Dyon J Don Kiwi van Vreumingen's user avatar
5 votes
2 answers
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Pauli Identity Using Tensor Network Notation

I am trying to understand the meaning of the equation shown in the above image taken from this paper, but I am unfamiliar with the tensor network notation. My current strategy is trying to write down ...
Calvin Liu's user avatar
3 votes
1 answer
396 views

What are Tensor Networks and which is the relationship they have with quantum computing?

I have been active in this community a while and I repeatedly see questions and answers referring to the so-called Tensor Networks. That makes me wonder what are those elements are and what the ...
Josu Etxezarreta Martinez's user avatar
3 votes
2 answers
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Qualitative meaning of the bond dimension of a matrix product state

Consider a matrix product state (MPS) with a bond dimension $D$. What is the physical intuition behind the bond dimension? Is it, in any way, related to the spatial geometry? In this note, it is ...
BlackHat18's user avatar
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How to find the $A_i$ in the matrix product state representation?

From what I understand, MPS is just a simpler way to write out a state, compared to the density matrix. But how do I get those $A_i$ matrices? From all the examples I read, people just somehow "...
Jack Nathan's user avatar
3 votes
1 answer
158 views

What is the computational cost of simulating a quantum circuit with matrix product states?

If we simulate Quantum circuits with the Matrix Product State (MPS) technique, the computational cost of the simulation depends on the entanglement in the circuit. How can I calculate this quantity ...
stopper's user avatar
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Injective Matrix Product State

I am going through a review on Tensor Networks and came across these statements: . This was a bit quick for me. I understand an injective MPS as one in which viewing $A$ as a map from auxiliary space ...
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Clock matrix vs matrix clock

In the process of research leading up to my previous question, I found out about matrix, vector & logical clocks. The citation in the aforementioned question mentions clock and shift matrices. ...
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2 votes
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How Mature is the Tensorflow Quantum Library [closed]

Where does The Tensorflow Quantum ( TFQ ) library fall on it's maturity curve. In other words can we currently leverage the TFQ ...
Darien Schettler's user avatar
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1 answer
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Truncating the bond dimension of an MPS -- how good is the approximation?

$\newcommand{\complex}{\mathbb{C}}\newcommand{\ket}[1]{|#1\rangle}$ Let $\ket{\psi}\in(\complex^d)^{\otimes n}$ be a pure quantum state. It is well-known that $\ket{\psi}$ is a matrix product state ...
Ben's user avatar
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2 answers
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How to convert a quantum circuit into a tensor network?

I need to perform tensor network contraction on a maxcut circuit, are there any resources or code available which converts maxcut circuit into a tensor network (preferably the adjacency list or any ...
Vishnu Vardhan's user avatar
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Reshaping the 4x4 CNOT gate into 2x2x2x2 in a tensor network

I'm learning how to perform tensor network contraction for simulating a quantum circuit by looking at the documentation for the JET simulator: link. Specifically, I'm trying to do all the calculations ...
Mao's user avatar
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1 answer
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Framework for PEPS of Surface Code

I am reading this article about the implementation of Surface Code with noise in PEPS tensor network. I am looking for a framework/library (preferred python) that is the nearest for such an ...
Ron Cohen's user avatar
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1 vote
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Plot circuit within TensorCircuit

Given an arbitrary TensorCircuit, is there a convient way to get a plot of the circuit?
user22285's user avatar
1 vote
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Tensor network simulation of quantum circuits with Python

What are the best tensor network-based simulators libraries in Python? In particular, I'm interested in calculating the expectation value of an observable measured at the end of a quantum circuit. ...
stopper's user avatar
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1 vote
1 answer
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How can I conceptualize virtual indices used in the time evolving block decimation (TEBD) algorithm?

I am trying to work with the Heisenberg $XX$ model which the Hamiltonien is given by $\hat{H} = -J \sum_i \left(\hat{X}_i\hat{X}_{i+1} + \hat{Y}_i\hat{Y}_{i+1}\right), \quad J > 0.$ Using $s^+ = |{...
Jean-Gabriel Chenard's user avatar
1 vote
1 answer
230 views

Exact expectation value of a quantum circuit simulated with the matrix product state method in qiskit

If I use the matrix product state method in Qiskit to simulate quantum circuits, I can obtain the exepctation value of an observable by using a finite amount of shots. Is there a way to obtain the ...
stopper's user avatar
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1 vote
1 answer
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Use state vector simulator with TensorCircuit

Is there a option to use instead of tensor network contraction state vector simulator for quantum circuits? This might be useful for small sized circuits, but I would still like to use TensorCircuit s....
user18722294's user avatar
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Paper concerning distributing quantum computation on many small quantum computers

I remember reading a paper that described how a quantum circuit on a large amount of qubits can be simulated by doing many runs on a smaller quantum computer. They used techniques from tensor networks....
John's user avatar
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1 answer
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Left-canonical matrix product state

A pure quantum state $$\tag{1}|\Psi\rangle=\sum_{j_1,\ldots,j_N=1}^{d}\psi_{j_1j_2\ldots j_N} |j_1, \dots, j_N\rangle\,,$$ can be represented exactly in the MPS form \begin{equation}\tag{2} |\Psi\...
jayjay's user avatar
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Trotterized time-evolution with tensorcircuit

I would like to do a Trotterized time-evolution with Tensorcircuit of a spin-Hamiltonian and started with the example https://github.com/tencent-quantum-lab/tensorcircuit/blob/master/examples/...
MatthiasN's user avatar
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Tensor network to simulate a specific final entry state

A tensor network can be used to simulate a quantum circuit, especially when we only want the probability of a specific entry (Ex: $|0110\rangle$) but not the full probability of all $2^n$ entries. Can ...
劉承瀚's user avatar
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1 answer
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Understanding PEPS Tensor Network for Surface Code

I am reading this article on page 2, and trying to understand the meaning of building of $W(C)$, and the reason for analogy. Why there are 2 indices $i$ and $i'$ for the physical indices? what is the ...
Ron Cohen's user avatar
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Folded MPS state with Mid-circuit measurement

Among some documents I found to make a MPS state on quantum circuit, I can make it with stepped arrangement of unitary operators. ...
gojo's user avatar
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3 answers
216 views

Specify bond dimension in tensor network simulation of quantum circuit (python)

I'm looking for a Python library that can help me simulating quantum circuit using Tensor Networks. In particular I would like to write a quantum circuit using the constiuent quantum gates and then ...
stopper's user avatar
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