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Questions tagged [state-tomography]

For questions about quantum state tomography, that is, the process of fully characterizing a quantum state from experimental measurements.

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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
11 votes
2 answers
734 views

In shadow tomography, how is the state reconstructed from its shadows?

I'm reading Huang et al. (2020) (nature physics), where the authors present a version of Aaronson's shadow tomography scheme as follows (see page 11 in the arXiv version): We want to estimate a state $...
glS's user avatar
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9 votes
2 answers
580 views

Why is the complexity of $n$-qubit state tomography not upper bounded as $O(3^n)$?

Consider the task of fully determining an $n$-qubit state $\rho$ which can be written as \begin{equation}\tag{1} \rho = \sum_{p \in \{I, X, Y, Z\}^n} \text{Tr}(\rho P_{p}) P_{p} \end{equation} and ...
forky40's user avatar
  • 6,908
9 votes
2 answers
281 views

How to know if your gate set is "complete"

In Daniel Greenbaum's paper, "Introduction to Gate Set Tomography", in page 20, he claims the gate sets $G = \{\{\}, X_{\pi/2}, Y_{\pi/2}\}$ and $G' = \{ \{\}, X_{\pi/2}, Y_{\pi/2}, X_{\pi}\}...
Cuhrazatee's user avatar
8 votes
1 answer
3k views

How to perform quantum state tomography on two qubits?

I would like to do a quantum tomography on two qubit states. Recently, I successfully did so for one qubit based on Nielsen-Chuang. They advise to use this formula for one qubit density operator ...
Martin Vesely's user avatar
8 votes
2 answers
1k views

What's the POVM corresponding to single-qubit state tomography?

Let $\rho$ be a single-qubit state. A standard way to characterise $\rho$ is to measure the expectation values of the Pauli matrices, that is, to perform projective measurements in the three mutually ...
glS's user avatar
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8 votes
1 answer
500 views

Using Classical Shadow to predict quantum state's fidelity has nothing to do with the dimension of the density matrix?

Using classical shadow(or refer to this post for basic things about classical shadow), we can predict linear functions like $Tr(O\hat{\rho})$ with number of copies(referred paper): $$ 2\log(2M/\delta)*...
narip's user avatar
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7 votes
1 answer
485 views

Are SIC-POVMs optimal for quantum state reconstruction?

Mutually unbiased bases (MUBs) are pairs of orthonormal bases $\{u_j\}_j,\{v_j\}_j\in\mathbb C^N$ such that $$|\langle u_j,v_k\rangle|= \frac{1}{\sqrt N},$$ for all $j,k=1,...,N$. These are useful for ...
glS's user avatar
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7 votes
1 answer
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How to calculate the fidelity of a certain gate of a IBMQ device in Qiskit using randomized benchmarking/tomography?

For example, I want to calculate the fidelity of a 1-qubit and 2-qubit gates (similar to the result shown in figure 2 in this paper). Is there any way to do that in Qiskit? I've gone through the ...
Trong Duong's user avatar
7 votes
1 answer
808 views

Quantum algorithm for linear system of equations (HHL) - Final Step: How can I find my vector of solution $|x\rangle$?

I'm working on solving a linear system with the quantum algorithm HHL. I don't understand how I can recover my vector $|x\rangle$ of real solution of the system starting from the states measured with ...
Nicolò Cangini's user avatar
7 votes
0 answers
73 views

If we could only get two-qubit tomography as an output, what algorithms are possible

According to the circuit model, the output for a quantum computation on $n$ qubits is an $n$-bit string. But what if we instead got a full two qubit tomography for all $n(n-1)$ pairs of qubits? This ...
James Wootton's user avatar
6 votes
1 answer
200 views

Lower bounds on the number of measurements outcomes required for quantum state tomography

It seems that in order to reconstruct a quantum state, a large number of measurements is typically used. Are there any known theoretical lower bounds on the number of measurements required to ...
Haim's user avatar
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6 votes
1 answer
490 views

Does computing the quantum mutual information $I(\rho^{AB})$ require full tomographic information of $\rho^{AB}$?

In the discussions about quantum correlations, particularly beyond entanglement (discord, dissonance e.t.c), one can often meet two definitions of mutual information of a quantum system $\rho^{AB}$: ...
Ilya's user avatar
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6 votes
1 answer
828 views

Implement the classical shadow coding error?

I'm trying to reproduce the basic method of classical shadow, which is based on the tutorial of pennylane. However, I've met some realization problems here when I finish reading the tutorial of ...
narip's user avatar
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6 votes
1 answer
149 views

Why does full state reconstruction require at least $N+1$ MUBs?

Consider an $N$-dimensional space $\mathcal H$. Two orthonormal bases $\newcommand{\ket}[1]{\lvert #1\rangle}\{\ket{u_j}\}_{j=1}^N,\{\ket{v_j}\}_{j=1}^N\subset\mathcal H$ are said to be Mutually ...
glS's user avatar
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6 votes
0 answers
262 views

Quantum State Tomography Implementation in IBMQ

I am working to understand quantum state tomography, specifically using the algorithm presented in PRL 108, 070502. This paper is referenced in IBMQ implementations of QST, both in old deprecated ...
Nathan Miller's user avatar
6 votes
0 answers
133 views

Weak Schur sampling and state distinguishability

Consider the task of distinguishing between the following two $n$ qubit quantum states. $$ \rho = \frac{\mathbb{I}}{2^{n}}.$$ $$ \sigma = \frac{1}{2^{n/2}}\sum_{x \in \{0, 1\}^{n/2}} |x\rangle\langle ...
BlackHat18's user avatar
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6 votes
0 answers
152 views

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
5 votes
2 answers
2k views

Is there a circuit to compare two quantum states?

Lets have two quantum states (single qubits ones for simplicity) $|\psi\rangle$ and $|\phi\rangle$: $$ |\psi\rangle = \alpha_\psi|0\rangle+\mathrm{e^{i\varphi_\psi}}\beta_\psi|1\rangle $$ $$ |\phi\...
Martin Vesely's user avatar
5 votes
1 answer
1k views

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
5 votes
2 answers
546 views

Give an explicit example of a $d = 4$ SIC-POVM

For $q=e^{2 \pi i/3}$, the set of $d^2$ vectors ($d=3$) \begin{equation} \left( \begin{array}{ccc} 0 & 1 & -1 \\ 0 & 1 & -q \\ 0 & 1 & -q^2 \\ -1 & 0 & 1 \\ -q &...
Paul B. Slater's user avatar
5 votes
1 answer
131 views

Unknown quantum circuit symbol

I was reading DiCarlo, L., Reed, M., Sun, L. et al. Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 467, 574–578 (2010). https://doi.org/10.1038/...
ryanhill1's user avatar
  • 2,503
5 votes
3 answers
269 views

What are the best-known lower bounds on the number of measurements required for quantum state tomography?

I'm very curious to know more about bounds of number of measurements (or number of independent copies of state) required to reconstruct full density matrix $\rho$ such that it is $\epsilon$-close (...
Jon Megan's user avatar
  • 497
5 votes
2 answers
1k views

What is the IQ plane?

I struggle to find any information on Nielsen and Chuang or similar texts on the exact definition of the so-called IQ plane (I think this is a notion closely related to solid state quantum computers ...
Marion's user avatar
  • 625
5 votes
1 answer
346 views

Problem with quantum tomography on two qubits

With reference to question on how to do quantum tomography on two qubits, I would like to ask you for help again. I tried to do the tomography on state \begin{equation}\psi=\frac{1}{2}\begin{pmatrix}...
Martin Vesely's user avatar
5 votes
0 answers
78 views

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
4 votes
2 answers
743 views

How to measure the sign of quantum amplitudes

I have a quantum state on $ n $ qubits ($ 2^n $ amplitudes) for which I know the amplitudes are real numbers. I want to take the state out as a vector. I can estimate the magnitude of the amplitudes ...
Sorin Bolos's user avatar
4 votes
1 answer
244 views

What are the problems of linear inversion quantum state tomography?

Consider the following general formulation of the standard quantum state tomography problem: given an unknown state $\rho$, a set of (known) observables $\{\mathcal O_k\}_k$ (generally the elements of ...
glS's user avatar
  • 25k
4 votes
1 answer
129 views

What are the conditions under which an unknown quantum state is learnable with arbitrary precision?

Assume that we have an unknown quantum state and we need to learn that unknown state with arbitrary precision. Under what conditions can we learn the unknown state with arbitrary precision? One ...
vivek kumar's user avatar
4 votes
2 answers
170 views

When perform tomography, do I get back to the classical information $\alpha_1,\alpha_2,\beta_1,\beta_2$ that I embedded in qubit?

Imagine I have a classical data(normalised to fit qubit) in the form of$\alpha_1,\alpha_2,\beta_1,\beta_2$ I assumed data to be in qubit $$\left| \psi \right> = (\alpha_1 + i\alpha_2 ) \left|0\...
User1086's user avatar
4 votes
1 answer
158 views

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 ...
Marion's user avatar
  • 625
4 votes
0 answers
57 views

How does the quantum Fisher information provide bounds for the estimation of output states?

Assume you have some quantum process $Q$ (e.g. quantum state tomography) that intakes initialised states $\rho_{i}$, $i=1,\ldots,n$ and gives some output $\rho'_i$. $$ \rho_1 \to Q \to \rho'_1 \\ \...
Marion's user avatar
  • 625
4 votes
1 answer
299 views

Numerical quantum state tomography simulator

On a classical computer, I want to simulate a learning-based quantum state tomography of a qubit. We can formulate it as finding a parametrized unitary evolution that takes the unknown pure state to a ...
New Developer's user avatar
3 votes
2 answers
371 views

Can quantum state tomography break bb84?

I am currently reading through this paper and read some of the wikipedia pages on weak measurement and quantum tomography and I am curious if weak measurement could be used to break BB84 quantum key ...
Quantum Guy 123's user avatar
3 votes
2 answers
567 views

Implementation of tomography on IBM Q

I wanted to ask how do you implement a circuit that finds the non-diagonal values of the density matrix of a quantum state on IBM Q?
Vladimir kozlov's user avatar
3 votes
1 answer
141 views

How to sample from a unitary 2-design?

How do we actually go about sampling from a unitary 2-design? Because the size of the 2-design grows quickly with the number of qubits, it seems challenging to sample. Some of the references I've ...
C. Kang's user avatar
  • 1,716
3 votes
2 answers
83 views

In what sense does quantum tomography "determine the state prior to the measurements"?

I have come across the term quantum tomography which, according to Wikipedia, is the [...]process by which a quantum state is reconstructed using measurements on an ensemble of identical quantum ...
aghin00's user avatar
  • 129
3 votes
2 answers
103 views

Optimising state tomography for fully entangled states

As tomography methods are usually inefficient, it's interesting to find good approximation. I was wondering the following: Assume one wants to estimate a state $\rho$ on $n$-qubits. Given a basis of ...
Daniele Cuomo's user avatar
3 votes
1 answer
1k views

How to do state tomography when using sampling in Qiskit?

Could anyone please explain how do I do state tomography when using sampling (on real device or QASM) in Qiskit? I know there's a special method for this, but I could not find a working example. More ...
mavzolej's user avatar
  • 1,941
3 votes
2 answers
349 views

Calculating bipartite state from joint probability distribution

We can calculate single qubit state by measuring it in pauli observables {$\sigma_{x},\sigma_{y},\sigma_{z}$} and then looking at its probability distribution. How to do this when we are having joint ...
Omkar 's user avatar
  • 331
3 votes
2 answers
100 views

Can you reconstruct some $N$-qubit entangled state only from ($N$-1) qubits?

Imagine that I have a Bell state of two qubits. If I can produce many copies (always of the same state) but I am allowed only to measure one of the qubits, I would be able to tell that the two qubits ...
Mauricio's user avatar
  • 2,326
3 votes
1 answer
116 views

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 ...
user1936752's user avatar
  • 2,935
3 votes
1 answer
403 views

Expansion of multi-qubit density matrix in the Pauli matrix basis

The single qubit density matrix can be expanded as $$ \rho=\frac{tr(\rho)I+tr(X\rho)X+tr(Y\rho)Y+tr(Z\rho)Z}{2} $$ which can be shown as, $\rho$ is a positive operator with $tr(\rho)=1$, ie., $\rho=\...
Sooraj S's user avatar
  • 821
3 votes
1 answer
168 views

state_tomography_circuits error

I build a QuantumCircuit named qc, I want to generate state tomography circuits to evaluate fidelity of simulation. I used code, ...
Jie Jiang's user avatar
3 votes
1 answer
233 views

How can one estimate the von Neumann entropy of an unknown quantum state?

Given many copies of some unknown quantum state $\rho$, I would like to compute its von Neumann entropy $S(\rho)$. What algorithm could be used for this that minimizes the number of copies required? ...
Gomez's user avatar
  • 33
3 votes
0 answers
100 views

Individual processing of quantum circuit measurment results

When superconducting transmon qubits are measured with a readout pulse, the raw readout signal is demodulated, and results appear as clouds on the IQ plane, with one point in the cloud representing ...
psitae's user avatar
  • 1,340
3 votes
0 answers
46 views

How to quantify trace distance between two matrices representing two quantum optical networks?

This is my first post here, so I'm sorry if this question could be ill-formulated. I have performed measurements on a 12x12 optical quantum network, so that I have a stochastic matrix $P^{exp}$ where ...
v_enushk's user avatar
2 votes
1 answer
201 views

Why can any density operator be written this way? (quantum tomography)

From page 24 of the thesis "Random Quantum States and Operators", where $(A,B)$ is the Hilbert-Schmidt inner product: \begin{aligned} \rho &=\left(\frac{1}{\sqrt{2}} I, \rho\right) \frac{...
Quantum Guy 123's user avatar
2 votes
2 answers
237 views

State tomography on a subsystem of the GHZ state

Premise: I am not sure whether I am missing something theoretically. Given a circuit creating a GHZ state over 3 qubits, say q1, q2 and q3. If I do not consider q3 and perform a state tomography over ...
Daniele Cuomo's user avatar
2 votes
1 answer
707 views

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: ...
quest's user avatar
  • 636