13 votes
Accepted

How Mature is the Tensorflow Quantum Library

First we should take a step back. Is there any machine learning done a quantum computer that cannot be efficiently simulated on a classical computer? The answer currently (2020) is no. In this ...
dabacon's user avatar
  • 695
7 votes
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Is Density Matrix simulation same as Tensor Network simulation?

A state vector on $n$ qubits is a $2^n$ complex number representing a system in a pure state. A density matrix on $n$ qubits is a $2^n$ by $2^n$ matrix representing a system in a mixed state. Mixed ...
dabacon's user avatar
  • 695
4 votes

Categories and types of quantum inspired algorithms

My reply is by no means an answer to your question. However, I still would like to drop in my 2 cents. The notion of "quantum-inspired" algorithms has no formal definition and has a rather ...
MonteNero's user avatar
  • 2,511
4 votes

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

A tensor is a multi-dimensional array. A vector is a 1d tensor, a matrix is a 2d tensor, and so forth. Tensor contraction is a generalization of matrix multiplication. In matrix multiplication, you ...
Craig Gidney's user avatar
  • 37.1k
4 votes

What can tensor networks mean for quantum computing?

A Different Way Of Looking At Linear Algebra Tensor Networks provide a different way of looking at linear algebra particularly within the context of tensor space systems. Quantum Circuits Are Just ...
Jake Xuereb's user avatar
3 votes

How to convert a quantum circuit into a tensor network?

Quantum circuits are effectively already a special type of tensor networks. We just need to interpret them appropriately to see this. Normally, we think of lines as representing qubits and boxes as ...
Adam Zalcman's user avatar
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3 votes
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Truncating the bond dimension of an MPS -- how good is the approximation?

The answer is found in F. Verstraete and J.I. Cirac, Matrix product states represent ground states faithfully, Lemma 1 on pg. 5 in the arxiv version. It states that the total error in approximating a ...
Norbert Schuch's user avatar
3 votes

How to split a 2-local unitary operator through singular value decomposition?

If I understand what you are asking for (I don't know much about tensor networks), both equations are singular value decompositions of $U$, just with respect to different indices (and in the latter ...
glS's user avatar
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2 votes
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How to find the $A_i$ in the matrix product state representation?

Any state can be written as a matrix product state. There are systematic procedures to construct such a description, based on sequential SVDs, see e.g. Section 4.1.3 of this review. On the other hand, ...
Norbert Schuch's user avatar
2 votes

Plot circuit within TensorCircuit

Suppose c is the circuit object, c.tex() will return the latex string using quantikz package, and ...
Simon's user avatar
  • 141
2 votes
Accepted

Qualitative meaning of the bond dimension of a matrix product state

The bond dimension across any link is precisely the Schmidt rank of the state across that cut. (Or potentially larger, if you chose a not-so-smart parametrization.)
Norbert Schuch's user avatar
1 vote

Left-canonical matrix product state

Iterative SVDs of the rank-$N$ coefficient tensor $\psi$ (see Eq. (1)) result in the representation of the quantum state as an MPS of the form written in Eq. (2). For a left-canonical MPS, let $A^{[...
jayjay's user avatar
  • 111
1 vote

Tensor network simulation of quantum circuits with Python

In Qiskit, if you want to compute the expectation value of a given operator $\hat{O}$ using the matrix_product_state-based simulation, you can use the primitive <...
SimoneGasperini's user avatar
1 vote
Accepted

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

A matrix product state is an ansatz for a wavefunction, and it can be used for modeling the qubits associated wtih any circuit, depending on your desired accuracy. If you want all amplitudes in the ...
user1271772 No more free time's user avatar
1 vote

How can I conceptualize virtual indices used in the time evolving block decimation (TEBD) algorithm?

I think this seems to be more a python problem. See an explanation of the numpy tensordot function here: https://stackoverflow.com/questions/41870228/understanding-tensordot Regarding your question, I ...
physicsprune's user avatar
1 vote

Plot circuit within TensorCircuit

@Simon's answer is absolutely correct. I just want to add a few details. When TensorCircuit transforms the circuit into Qiskit's QuantumCircuit, non-unitary ...
Egretta.Thula's user avatar
1 vote

Qualitative meaning of the bond dimension of a matrix product state

I don't know if the bond dimension is related to the spatial dimension of many-body systems. As I understand it from this note, the bond dimension can be viewed as a 'refinement parameter', ie the set ...
francois-marie's user avatar
1 vote

Pauli Identity Using Tensor Network Notation

I would read the picture from left to right, as a quantum channel acting on density matrices -- here, the lower layer is ket, and the upper bra. Then, the left side is the identity map $$ \mathcal ...
Norbert Schuch's user avatar
1 vote
Accepted

Pauli Identity Using Tensor Network Notation

In your computation of the RHS of the equation, you treat the two $\sigma$s as if they were a tensor product of two 1-qubit operators, whereas you should consider the first as an effet (the dagger of ...
Renaud Vilmart's user avatar
1 vote

What can tensor networks mean for quantum computing?

By treating a quantum circuit as a network model, the network model can be optimized the order of the calculation by making a contract between tensor and tensor. I think it is definitely important to ...
gojo's user avatar
  • 29

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