Questions tagged [quantum-process-tomography]

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.

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Process matrix of CNOT gate

The fig below is the process matrix of the CNOT gate from this paper: where the legend explains that red corresponds to $\frac14$, green to $-\frac14$ and white to zero. I know the $U_{CNOT} = \frac{...
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Derive $\text{tr}((P_A\otimes P_B)\rho_\mathcal{E})=\frac{1}{d}\text{tr}(P_A\mathcal{E}(P_B^*))$

The estimate expectation values is $$\text{tr}((P_A\otimes P_B)\rho_\mathcal{E})=\text{tr}((P_A\otimes P_B)(\mathcal{E}\otimes I)(|\psi\rangle\langle\psi|))\,,$$ where $P_A$ and $P_B$ are Pauli ...
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Problem with orthogonal traceless Hermitian matrices

In the compressive QPT method, the trace-preserving constraint of the process matrix is $\sum_{n, m} \chi_{n m} \Upsilon_m^{\dagger} \Upsilon_n=1$. In this paper:https://arxiv.org/abs/1404.2877, as $\...
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Is a process matrix of rank $1$ unique?

It is said that when an unknown process is unitary, its $\chi$ matrix is rank-$1$ and possesses only one positive eigenvalue. See eg https://arxiv.org/abs/2306.07867. So when the process matrix has ...
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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: ...
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Why does the process matrix $\chi$ have dimensions $d^2\times d^2$?

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 $\chi$ ...
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I have two Choi matrix I suspect be equivalent. Can I manipulate them?

I am performing a process tomography over a protocol I suspect to be equivalent to the $CS$ gate. To compare basic operators I usually compute the Choi matrix of the target gate -- which in this case ...
Daniele Cuomo's user avatar
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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 $\chi$ ...
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Quantum Process Tomography for 2 qubits

I need clarification on a few aspects related to Box 8.5 and Exercise 8.34 from the book Quantum Computation and Quantum Information by Nielsen & Chuang . While attempting Exercise 8.34, I ...
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How can I compute the probability distribution by using channel through Choi matrix in quantum process tomography?

The probability of observing an outcome corresponding to $M_j$ (a positive measurement operator), when the quantum process has transformed some input state $\rho_j$ is $p_{ij}=tr[\mathcal{E}(\rho_i)...
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Is there a tight operator frame that is also a POVM?

We define the tight operator frame as a set of operators $\{E_i\}_{i=1}^{n}$ satisfying \begin{equation} \sum_{i=1}^n \vert \langle \langle E_i \vert X \rangle \rangle \vert^2 = C \Vert V \Vert_2^2, \...
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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 ...
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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 ...
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How to calculate the Pauli Noise model of a physical gate operation?

I've seen literature and QuTip implementation of calculating a gate fidelity given the transformed density matrix, and in that case it uses a number of different initial states. My question however, ...
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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 ...
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Non-local $CNOT$ By means of Ising gates

Consider the circuit below. This is almost the same as the standard protocol to perform a non-local $CNOT_{0,3}$. The only difference is that I decomposed the upper local $CNOT_{0,1}$ into one Ising ...
Daniele Cuomo's user avatar
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How is the $\beta$-matrix interpreted in single qubit QPT?

In Chapter 8 of Quantum Computation & Quantum Information by Nielsen & Chuang, more precisely Box 8.5, there is an example of quantum process tomography for a single qubit. (The same ...
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Prove $\beta=\Lambda\otimes\Lambda$, where $\Lambda=\dfrac{1}{2}\begin{bmatrix}I&X\\X&-I\end{bmatrix}$ for single qubit tomography

In the Section on single qubit quantum process tomography, Box 8.5, Page 393, Chapter 8, Quantum Computation and Quantum Information by Nielsen and Chuang, and in Prescription for experimental ...
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Why is $\chi$ not uniquely determined by $\sum_{mn}\beta_{jk}^{mn}\chi_{mn}=\lambda_{jk}$?

The mathematical construct of the Quantum process tomography is given in Page 391, 392, Chapter 8, Quantum Computation and Quantum Information by Nielsen and Chuang, as follows Let a fixed set of ...
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How to derive the number of independent parameters in the $\chi$ matrix from the Choi matrix?

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 $d^4−d^2$ ...
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How to extract the entanglement fidelity from an arbitrary quantum operation?

I have an arbitrary process matrix that does an entangling operation (a controlled-pi/2 rotation) plus some additional phase rotations that are not of interest. I am curious to find a way to extract a ...
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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 $d^4−d^2$ ...
Sooraj S's user avatar
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In quantum process tomography for one and two qubit, why can we express the $\chi$ matrix in this form?

I'm reading Nielsen and Chuang and I read quantum tomography process given by N&C (box 8.5), which provides an algorithm for determining $\chi$ in terms of block matrices and density matrices. And ...
username9's user avatar
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Quantum process tomography, non-trace preserving

Consider an unknown quantum process, i.e., a black box, acting on a physical quantum system described by a density matrix $\rho$ associated with a d-dimensional Hilbert space $\mathcal{H}$. A complete ...
username9's user avatar
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How to merge logical computation with encoding-decoding schemes

Usually QEC is treated in two different ways. Definition of a logical computation with a non-destructive QEC scheme Definition of a encoding-decoding scheme with destructive measurement after ...
Daniele Cuomo's user avatar
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Optimising Tomography on logical computation

I already got part of the answer in thread. Which says that if I want to perform a state tomography on a known state, the estimation can be simplified. In the case of "GHZ-class", citing ...
Daniele Cuomo's user avatar
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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: ...
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How to compute the unitary from the $\chi$ matrix obtained from QPT

I am trying to do quantum process tomography for one qubit and obtain the unitary for the gates that are applied on the qubit. I have studied the theory on process tomography from mike and ike and the ...
Parmeet Singh EP 066's user avatar
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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&...
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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 ...
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Process Tomography for Blind Quantum Computation

Process Tomography can identify the quantum channel, while Blind Quantum Computation strives to hide the inputs using quantum gates. Given the user executes the same blind circuit multiple times (of ...
Aritra's user avatar
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In quantum process tomography, how does $\chi$ characterize a quantum process?

I'm working through Nielsen and Chuang and I'm pretty confused by the discussion of quantum process tomography. I'm trying to work through an example of 1-qubit state tomography given by N&C (box ...
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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 ...
Quantum Guy 123's user avatar
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What is the best method for estimating average channel fidelity?

This thesis shows an efficient way to estimate average channel fidelity (in chapter 4). However, it is somewhat old (from 2005). Are there any better methods out there? By better I mean: are there ...
Quantum Guy 123's user avatar
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Can Gate Set Tomography work on Quantum Channels?

I stumbled across a new paper on gate set tomography. Can gate set tomography be applied to a quantum channel or multiple quantum channels? Will the same advantages still apply of not having to 'rely ...
Quantum Guy 123's user avatar
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Can you perform quantum process tomography using an orthonormal basis the contains non Hermitian matrices?

In the thesis "Efficient Simulation of Random Quantum States and Operators" on page 25 there is a portion of text explaining a method for quantum process tomography. It claims that states ...
Quantum Guy 123's user avatar
6 votes
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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 ...
Oliver Müller's user avatar
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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 ...
tap86's user avatar
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How to measure a general two-qubits gate? Does it help to Bob and Alice?

Excuse me if this question is absurd. I discovered logic gates a few weeks ago. two-qubis Logic gates are represented by 4x4 matrices. Can they mimic a general density matrix of pairs of spin 1/2 ...
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Why the chi-matrix fidelity of the process is the fidelity of the chi-matrix noise map

I am following this paper, and I am stuggling with a derivation. Basically, I consider an orthonormal basis $\{B_i \}$ with respect to Hilbert-Schmidt scalar product, on the density matrix space $\...
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Is it possible to partial trace the $\chi$-matrix of $4$ qubits $q_0,q_1,q_2,q_3$ to obtain a description of what happens to $q_1$?

Considering a $\chi$-matrix of a circuit with, say, 4 qubits, is it possible to trace out 3 of them from $\chi$ - for example qubits $q_0$, $q_2$ and $q_3$ - thus gaining the process matrix describing ...
Daniele Cuomo's user avatar
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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 ...
Daniele Cuomo's user avatar
5 votes
1 answer
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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 ...
Pralekh Dubey's user avatar