Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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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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 $\rho$. We apply a number of random unitary…
glS
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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 ProcessTomographyFitter class. Documentation states that such function gives a Choi matrix as output.…
Daniele Cuomo
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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 each $P_{p} = P_{p_1} \otimes \dots \otimes…
forky40
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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 $G' = \{ \{\}, X_{\pi/2}, Y_{\pi/2}, X_{\pi}\}$ with $F_k \in G$, $F_k |\rho\rangle\rangle$ are able to…
Cuhrazatee
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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 estimation: \begin{equation} \rho =…
Martin Vesely
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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…
narip
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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 unbiased bases corresponding to the Pauli…
glS
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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 & 0 & 1 \\ -q^2 & 0 & 1 \\ 1 & -1 & 0 \\ 1 & -q & 0 \\ 1 & -q^2 & 0…
Paul B. Slater
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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 Qiskit Ignis documentation, but I didn't see if it's…
Trong Duong
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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 ancilla qubit in $|1\rangle$. I found something…
Nicolò Cangini
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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 a variety of reasons, e.g. because they provide…
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 pennylane, and trying to finish the method myself, just…
narip
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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\rangle =…
Martin Vesely
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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 would need to be calculated over many shots. If we…
James Wootton
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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 $\rho^{AB}$: $$ I(\rho^{AB}) = S(\rho^A) + S(\rho^B) -…
Ilya
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