For all questions regarding quantum process tomography or derivatives thereof (like gate-set tomography). In quantum process tomography, processes that are performed on qubits are characterized rather than the state of the qubits themselves; see quantum state tomography for this.
Questions tagged [quantum-process-tomography]
47 questions
11
votes
1 answer
What is the relationship between Choi and Chi matrix in Qiskit?
I'm struggling with the framework for quantum process tomography on Qiskit.
The final step of such a framework is running fit method of ProcessTomographyFitter class. Documentation states that such function gives a Choi matrix as output.…
Daniele Cuomo
- 2,068
- 10
- 25
6
votes
2 answers
Why does the $\chi$ matrix have $d^4-d^2$ independent parameters?
In the section on Quantum process tomography, Page 391, Chapter 8, Quantum Computation and Quantum Information by Nielsen and Chuang. it is given that
In general, $\chi$ will contain $d^4−d^2$ independent real parameters, because a general linear…
SOORAJ SOMAN
- 891
- 4
- 16
6
votes
0 answers
What is the best quantum process tomography method?
This question is somewhat related to this question. What is currently the best method for quantum process tomography? By best I mean, the one that can achieve the best accuracy of estimation per qubit used.
Quantum Guy 123
- 1,499
- 6
- 20
6
votes
0 answers
What is quantum tomography useful for?
First time poster and just started with quantum computing for my master thesis, so I'm sorry if the question seems obvious.
I understand that the tomography is used to reconstruct the state and/or process of a quantum circuit, without directly…
Oliver Müller
- 61
- 2
5
votes
1 answer
How can I fit an unknown quantum channel?
Suppose that I have one noisy channel $\mathcal{E}$ and I want to fit it with another one $\mathcal{E}_0(p)$ that depends on some fitting parameter $p$.
As both of this processes for me are represented by matrices, I would simply minimize the…
tap86
- 87
- 6
5
votes
1 answer
How to perform Quantum Process Tomography for three qubit gates?
I am trying to perform Quantum process tomography (QPT) on three qubit quantum gate. But I cannot find any relevant resource to follow and peform the experiment. I have checked Nielsen and Chuang's Quantum Computation and Quantum Information…
Pralekh Dubey
- 55
- 4
4
votes
1 answer
Quantum State Tomography from IQ plane data
Background:
I am given to understand that the steps of Quantum State Tomography (QST) are as follows for a single qubit:
The qubit is in the state $\psi=a_0|0\rangle+a_1|1\rangle$ with density matrix $\rho = |\psi\rangle\langle\psi|$.
Decompose…
Marion
- 695
- 3
- 14
3
votes
1 answer
Why is the Choi matrix I get for the depolarizing channel $\mathcal{E}(\rho) = (1 - p) \rho + p \frac{I}{2}$ different from what it shold be?
I'm currently trying to implement the depolarizing channel on qiskit. But, as I see in my calculation it doesn't match with the qiskit aer_noise.
So, for the Depolarizing Channel we got :
$$
\mathcal{E}(\rho) = (1 - p) \rho + p \frac{I}{2}
$$
Ant…
felipechoy
- 51
- 1
3
votes
0 answers
Why use 576 configurations for two-qubit process tomography?
In the paper "Efficient Measurement of Quantum Dynamics via Compressive Sensing" Shabani Et. al (2011) [arXiv:0910.5498], The full process tomography of two-photon is performed as: Preparing 16 pairwise combinations of the 4 input states…
karry
- 689
- 4
- 14
3
votes
2 answers
When should I use the Choi matrix and when should I use the $\chi$ matrix?
A quantum map on a $d$-dimensional space has the general representation:
$$
\mathcal{S}(\rho)=\sum_{\alpha,\beta}^{d^2}\chi_{\alpha\beta}\Gamma_{\alpha}\rho \Gamma_{\beta}^{\dagger},
$$
where $\chi$ is the $d^2\times d^2$ process matrix, which is…
karry
- 689
- 4
- 14
3
votes
1 answer
Alternatives to process tomography and gate set tomography
I need to characterize an unknown 2-qubit operation. As I understand it, quantum process tomography (QPT) can do this, but will not account for state preparation and measurement (SPAM) errors. On the other hand, gate set tomography provides a full…
jchadwick
- 493
- 2
- 10
3
votes
1 answer
Is tomography of the Choi state sufficient for channel tomography?
Given that there is an isomorphism between quantum states and quantum channels (the Choi-Jamiolkowski isomorphism) and given that state tomography is well-researched, why is quantum process or quantum channel tomography an interesting research…
user1936752
- 3,311
- 1
- 9
- 24
3
votes
1 answer
Does any quantum channel satisfy ${\rm Tr}(\mathcal E^\dagger \mathcal E) \in[0, d^2]$?
I am reading the paper "Direct Fidelity Estimation from Few Pauli Measurements".
According to the paper, the entanglement fidelity between the a unitary channel $\mathcal U$ and a quantum channel $\mathcal E$, is defined as
\begin{align}
F_e = {\rm…
Michael.Andy
- 599
- 3
- 8
3
votes
1 answer
How to find the Kraus operators from the process matrix?
I am trying to find the Kraus operator from process matrix.
For instance, suppose that for single qubit identity gate, I have the following process matrix:
[[1. , 0. , 0. , 0. ],
[0. , 0.937, 0.004, 0.005],
[0.023, 0.014, 0.935,…
quest
- 704
- 4
- 11
3
votes
3 answers
How to describe the evolution of a density matrix using the Choi matrix?
How do I apply the Choi matrix on a Density matrix.
Say my process is a Hadamard gate, and my input state is the ground state on 1 qubit (qubit id 0).
$U = H = \dfrac{1}{\sqrt{2}} \begin{bmatrix}1&1\\1&-1\end{bmatrix}$
Thus, to do ancilla assisted…
Aritra
- 323
- 1
- 8