Questions tagged [tomography]

Quantum tomography or quantum state tomography is the process of reconstructing the quantum state (density matrix) for a source of quantum systems by measurements on the systems coming from the source. (Wikipedia)

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1answer
784 views

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 ...
5
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1answer
469 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 ...
5
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0answers
31 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 ...
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2answers
160 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\...
4
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2answers
108 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 ...
4
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2answers
162 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 &...
4
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1answer
128 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}...
4
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1answer
80 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 ...
4
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1answer
144 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 ...
4
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1answer
166 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 ...
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2answers
185 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?
3
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2answers
144 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 ...
3
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1answer
296 views

Quantum tomography on two qubits

I would like to do a quantum tomography on two q-bit state. Recently, I successfully did so for one q-bit based on Nielsen-Chuang. They advise to use this formula for one q-bit density operator ...
3
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1answer
223 views

Total mutual information of a quantum system

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 $\rho^{AB}$: ...
3
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1answer
48 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? ...
2
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1answer
169 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 ...
2
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1answer
142 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 ...
2
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1answer
140 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 ...
2
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1answer
88 views

How is postselection used in quantum tomography?

I refer to this paper but reproduce a simplified version of their argument. Apologies if I have misrepresented the argument of the paper! Alice has a classical description of a quantum state $\rho$. ...
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0answers
40 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 ...
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2answers
93 views

How to distinguish two states with same density matrix using a quantum state tomography?

I tried to measure quantum state with a quantum state tomography. However, I encountered a situation when two different quantum states had the same density matrix. In particular, these states were $\...
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1answer
78 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?
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0answers
42 views

Adding Quantum State Tomography Step in Cirq HHL Algorithm Implementation

Over the past month, I have been learning about the HHL algorithm and am interested in extending the implementation provided here (https://github.com/quantumlib/Cirq/blob/master/examples/hhl.py) to ...
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1answer
34 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
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1answer
91 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 ...