Questions tagged [tomography]
For questions about quantum state tomography, that is, the process of fully characterizing a quantum state from experimental measurements.
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How to reconstruct the density matrix $\rho$ from the overlap matrix $T_{a,a'}={\rm Tr}(M^{(a)}M^{(a')})$?
Suppose we have $N$-qubit POVM
$${\bf M} = \{M^{(a_1)} \otimes M^{(a_2)} \otimes \cdots \otimes M^{(a_N)}\}_{a_1, \ldots, a_N}.$$
Given an $N$-qubit state $\rho$, the measurement outcome ${\bf a} = (...
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How to improve the state fidelity of state tomography in qiskit
I want to simulate state tomography on a 8 qubit state. I use the example https://qiskit.org/ecosystem/experiments/manuals/verification/state_tomography.html as a guide.
My problem is that I get a ...
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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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What are the estimate-estimate and estimate-project algorithms for quantum overlap?
In this paper on improvements to the traditional SWAP test to measure quantum state overlap (or fidelity), they mention two methods called estimate-estimate and estimate-project.
I googled about these ...
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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 ...
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How are mixed states given to a quantum algorithm?
I've been reading this paper about quantum fidelity estimation, but really have no idea what's going on when it comes to density matrix notation. In the abstract, they have the following quote:
...
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Trainning RBM with QuCumber
Does anyone here have any idea on how to use the python package QuCumber?
They seem really dead in the sense that in their GitHub page there are no updates for more than 4 years.
Anyway, I was reading ...
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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 ...
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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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Problem with qiskit only accepting ${\rm tr}(\rho^2)=1.$ while performing state tomography
I am performing state tomography after a computation cycle in order to store information about the state before measurement and use that information to re-initialise the state for the new cycle of ...
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Basic import problem for qiskit_experiments module, how to fix?
I'm trying to make use of the qiskit_experiments module but I always get a "No module named 'qiskit_experiments'" error while trying to import it. I've uninstalled and reinstalled qiskit in ...
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Qiskit state_fidelity not accepting my Density Matrices
I'm attempting to use qiskit's state_fidelity(state1, state2, validate=True) but keep getting the following error: QiskitError: 'Input quantum state is not a valid'
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Using Qiskit State Tomography on Subsystems
I have a version of the following circuit set up.
...
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What is optimum method for measuring the probability for all zero state given an arbitrary circuit using ancilla qubits and additional gates
Given some arbitrary quantum circuit, I want to measure the probability amplitude for the all zero state in an optimum manner, given possibly additional ancilla qubits and by applying additional ...
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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 ...
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Error with StateTomographyFitter
I am trying to perform a state tomography over a circuit of 5 qubits named circ.
I personally measure qubits 1,2 and 3. While the tomography is over qubits 0 and 4. ...
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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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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=\...
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Ensemble state identification from ensemble state distinction
I am trying to derive Fact 5. in paper 1:
Let $\mathscr{E}=\{\sigma_1,.., \sigma_m\}$ be an ensemble of quantum states in $\mathbb{C}^n$. If there is a POVM $\mathscr{M}$ for the state distinction ...
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Why is state discrimination possible to infidelity $\delta$ using $n=\Theta(1/\delta)$ states?
In (Haah et al. 2015), in the first section, the authors study the asymptotic behaviours of fidelity and trace distance between $\rho^{\otimes n}$ and $\sigma^{\otimes n}$ for some given pair of ...
glS♦
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State tomography with Pauli basis measurements for a high number of qubits
My end goal is to recover the quantum state in its computational basis or reduced density matrix of a high number qubit circuit in a real QPU. Taking into account that the number of qubits will be ...
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Does the maximum-likelihood estimation use all the measurement settings?
I see the words : "Given a fixed time
T during which an experiment can be run, is it better to do compressed tomography or full
tomography, i.e. is it better to do compressed tomography or full
...
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What is the difference between the complexity $O$-notation?
For a rank $r,d\times d$ density matrix $\rho$, where $d=2^n$, using $O(rdlog^2d)$ measurement settings can reconstruct the density matrix, while I see another description that we need $\Omega(rd\ \...
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How is a quantum state copied for tomography?
The no-cloning theorem prevents creation of independent copies of a quantum state.
And if we use CX gates we create entangled copies, which are affected by each others measurement.
So, how does one ...
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What is the rank of the pure state?
Consider pure or nearly pure quantum state, is it usually low-rank? Can you give a example of a concrete state and its rank?
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IBM Quantum Lab - Server unavailable or unreachable. Would you like to restart?
In the following circuit, I want to perform tomography on the qubits 0,1,2,3 after qubits 4,5,6,7,8,9 are measured.
I run the circuit using with measurement gates on qubits 4,5,6,7,8,9 with the ...
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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 ...
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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\...
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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 (...
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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 ...
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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 ...
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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 ...
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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, ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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):
$$
2\log(2M/\delta)*...
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What are the problems of linear inversion quantum state tomography?
Consider the following general formulation of the standard quantum state tomography problem: given an unknown state $\rho$, a set of (known) observables $\{\mathcal O_k\}_k$ (generally the elements of ...
glS♦
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Are SIC-POVMs optimal for quantum state reconstruction?
Mutually unbiased bases (MUBs) are pairs of orthonormal bases $\{u_j\}_j,\{v_j\}_j\in\mathbb C^N$ such that
$$|\langle u_j,v_k\rangle|= \frac{1}{\sqrt N},$$
for all $j,k=1,...,N$.
These are useful for ...
glS♦
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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 ...
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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 ...
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$\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 ...
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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 ...
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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 ...
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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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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 ...
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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 \\
\...
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