Questions tagged [tomography]

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

Filter by
Sorted by
Tagged with
0 votes
0 answers
68 views

Do quantum states with a single parameter give any theoretical or experimental advantage compared to multi-parameter ones?

If a quantum state is a single parameter two-qubit mixed entangled state then is there any theoretical or experimental advantage compared to a multi-parameter state? suppose, we take a single ...
user avatar
4 votes
0 answers
94 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 ...
user avatar
1 vote
2 answers
64 views

Is it possible to efficiently measure outer products of quantum states, of the form $|a\rangle\langle b|$?

I am looking at a matrix reconstruction algorithm that, given singular values $\sigma_i$ and quantum states $|u_i\rangle$ and $|v_i\rangle$ that are efficiently prepared on a quantum computer, ...
user avatar
  • 51
2 votes
1 answer
109 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: ...
user avatar
  • 406
2 votes
0 answers
48 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 ...
user avatar
  • 1,230
2 votes
0 answers
58 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 ...
user avatar
2 votes
0 answers
33 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 ...
user avatar
1 vote
0 answers
54 views

Confusion about the objective function of VQEs and QAOAs

I am a bit puzzled on how the objective function of the VQEs and QAOAs. Of course, the parametrised state is constructed differently in these two algorithms but they do share a common objective to be ...
user avatar
  • 409
5 votes
1 answer
99 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)*...
user avatar
  • 2,398
3 votes
1 answer
107 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 ...
user avatar
  • 18.2k
6 votes
1 answer
119 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 ...
user avatar
  • 18.2k
3 votes
1 answer
174 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 ...
user avatar
  • 2,398
0 votes
0 answers
18 views

Exacting specific results in running a list of tomography circuit

I run a test on tomography of two circuits like this: ...
user avatar
  • 51
7 votes
2 answers
170 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 ...
user avatar
  • 4,537
1 vote
1 answer
86 views

$\mu$ matrix construction for quantum state tomography

In the paper Maximum Likelihood, Minimum Effort, given an orthonormal Hermitian operator basis $\{\sigma_i\}_{i=1}^{d^2}$ of $d \times d$ matrices and a set of measured values $m_{ij}$ corresponding ...
user avatar
  • 2,576
4 votes
1 answer
83 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 ...
user avatar
0 votes
0 answers
112 views

Qiskit State Tomography with Additional Classical Register

For a circuit with a classical register like in the image, I cannot apply StateTomographyFitter(result, tomography_circuits).fit() method for the second and third ...
user avatar
  • 1
4 votes
1 answer
138 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 ...
user avatar
  • 207
3 votes
1 answer
72 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 ...
user avatar
  • 409
4 votes
1 answer
445 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 ...
user avatar
  • 409
3 votes
0 answers
34 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 \\ \...
user avatar
  • 409
5 votes
0 answers
53 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 ...
user avatar
2 votes
0 answers
48 views

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 ...
user avatar
0 votes
1 answer
80 views

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 ...
user avatar
1 vote
1 answer
88 views

how to implement Quantum tomography on an arbitrary state using Qiskit?

Can quantum tomography helps to reconstruct the state? How is this possible with arbitrary quantum state? For example if I have a $$|\psi\rangle= (0.24506+0.9633i)|0\rangle + (0.0046238+0.10943i)|1\...
user avatar
7 votes
2 answers
190 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}\}...
user avatar
3 votes
2 answers
419 views

What does the POVM corresponding to single-qubit state tomography look like?

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 ...
user avatar
  • 18.2k
2 votes
1 answer
103 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{...
user avatar
3 votes
2 answers
312 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 ...
user avatar
5 votes
0 answers
84 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 ...
user avatar
5 votes
1 answer
110 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/...
user avatar
  • 1,626
7 votes
2 answers
283 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 $...
user avatar
  • 18.2k
1 vote
1 answer
78 views

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 ...
user avatar
  • 165
4 votes
2 answers
684 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\...
user avatar
3 votes
1 answer
93 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? ...
user avatar
  • 33
6 votes
1 answer
117 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 ...
user avatar
  • 18.2k
3 votes
1 answer
569 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 ...
user avatar
  • 1,408
3 votes
2 answers
234 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 ...
user avatar
  • 311
4 votes
2 answers
303 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 ...
user avatar
2 votes
1 answer
189 views

Transferring GHZ state onto some qubits

This question is just my effort that I made by understanding the previous answers to my questions . I have a GHZ state $|000\rangle+|111\rangle$ (please ignore the normalizing constant). For ...
user avatar
  • 1,380
1 vote
0 answers
76 views

Adding Quantum State Tomography Step to HHL Algorithm (Cirq)

Over the past month, I have been learning about the HHL algorithm and am interested in extending the Cirq implementation to include the quantum state tomography step to extract the amplitudes or ...
user avatar
2 votes
1 answer
237 views

How to obtain the density matrix using tomography in the real device?

I am trying to run the QFT algorithm for n=5 (n number of qubits). The number of experiments that it generates is bigger than the one allowed by the IBM devices (i.e. 75). Therefore, I have tried to ...
user avatar
  • 339
7 votes
0 answers
51 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 ...
user avatar
9 votes
1 answer
938 views

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 ...
user avatar
1 vote
1 answer
84 views

Tomography library in Qiskit?

I am wondering what is the equivalent to the import bellow in the current version of Qiskit? import qiskit.tools.qcvv.tomography as tomography
user avatar
3 votes
1 answer
600 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 ...
user avatar
2 votes
0 answers
65 views

IBMQJob.result() returns KeyError: 'qObjectResult'

I'm running tomography job like I have done many times before. I send the job, and the job.status() is 'DONE'. But when I ask for ...
user avatar
  • 121
3 votes
2 answers
365 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?
user avatar
1 vote
1 answer
113 views

Is it possible to get the $\alpha$ and $\beta$ (amplitudes) of a qubit in Qiskit?

Is it possible to get the $\alpha$ and $\beta$ (amplitudes) of a qubit in Qiskit, i.e. not only probabilities after measurement but complete quantum state?
user avatar
5 votes
1 answer
205 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}...
user avatar