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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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11 votes
1 answer
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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 ...
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10 votes
2 answers
2k views

### 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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7 votes
0 answers
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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 ...
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5 votes
1 answer
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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 Qiskit provides a backend to simulate state-vectors and a backend for ...
5 votes
1 answer
197 views

### 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) ...
5 votes
2 answers
166 views

### 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 ...
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3 votes
1 answer
398 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 ...
3 votes
2 answers
454 views

### 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 ...
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3 votes
2 answers
392 views

### 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 ...
3 votes
1 answer
1k views

### 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 "...
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3 votes
1 answer
166 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 ...
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3 votes
0 answers
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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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3 votes
0 answers
322 views

### 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
1 answer
388 views

### 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 ...
2 votes
1 answer
547 views

### 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. ...
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2 votes
1 answer
275 views

### 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 ...
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2 votes
0 answers
37 views

### How can I increase number of qubits by increasing RAM/GPU?

I am using Qiskit, where if I go beyond 32 qubits, the output does not get counted. The code is not supported by the stabilizer back-end. I want to use up to 100+ qubits for my task. I got RAM 42 GB ...
2 votes
1 answer
248 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 ...
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2 votes
0 answers
435 views

### 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 ...
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2 votes
1 answer
100 views

### 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 ...
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1 vote
2 answers
110 views

### Plot circuit within TensorCircuit

Given an arbitrary TensorCircuit, is there a convient way to get a plot of the circuit?
1 vote
1 answer
85 views

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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. ...
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0 votes
3 answers
226 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 ...
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