Questions tagged [shadow-tomography]
The study of solutions to the following problem: given an unknown D-dimensional quantum mixed state ρ, as well as known two-outcome measurements E1,...,EM, estimate the probability that Ei accepts ρ, to within additive error ε, for each of the M measurements. How many copies of ρ are needed to achieve this, with high probability?
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Can a quantum state be certified using self-test?
I am reading the paper Certifying almost all quantum states with
few single-qubit measurements. The main result of the paper (Theorem 1) is that
given an $n$-qubit target pure state $|\psi\rangle$ and ...
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Are classical shadows useful?
according to the paper https://doi.org/10.1038/s42254-022-00535-2 , the advantage of classical shadows is doing measurements first and asking questions later.
But in real experiments, who would do ...
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Is there a tight operator frame that is also a POVM?
We define the tight operator frame as a set of operators $\{E_i\}_{i=1}^{n}$ satisfying
\begin{equation}
\sum_{i=1}^n \vert \langle \langle E_i \vert X \rangle \rangle \vert^2 = C \Vert V \Vert_2^2, \...
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Inverse channel of the Pauli 4 POVM
I'm currently grappling with a challenge in comprehending the inverse channel of the Pauli 4 POVM. The POVM elements are defined as follows:
$
M_0 = \frac{1}{3} |0\rangle\langle0|, \quad M_1 = \frac{1}...
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What is the mistake in this Qutip implementation of the classical shadows protocol (Huang et. al. 2020)?
So I'm trying to replicate the results from Huang's paper, following Pennylane's tutorial. But instead of using Pennylane (in particular their recently implemented ClassicalShadow class), I'm trying ...
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How are classical shadows stored efficiently?
The paper states that classical shadows can be stored efficiently by stabilizer formalism. But I'm confused what information is stored? I can't tell the efficiency come from.
In the paper，the ...
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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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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):
$$
2\log(2M/\delta)*...
- 3,109
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How do I pick a random Clifford operation in Stim?
I want to sample random n-qubit Clifford operations. How do I do that in Stim?
(Self-answering because this was requested when the feature already existed)
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Implement the classical shadow coding error?
I'm trying to reproduce the basic method of classical shadow, which is based on the tutorial of pennylane. However, I've met some realization problems here when I finish reading the tutorial of ...
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Why is the complexity of $n$-qubit state tomography not upper bounded as $O(3^n)$?
Consider the task of fully determining an $n$-qubit state $\rho$ which can be written as
\begin{equation}\tag{1}
\rho = \sum_{p \in \{I, X, Y, Z\}^n} \text{Tr}(\rho P_{p}) P_{p}
\end{equation}
and ...
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Inverting the depolarizing channel
I have a depolarizing channel acting on $2^n \times 2^n$ Hermitian matrices, defined as
$$\tag{1}
\mathcal{D}_p (X) = p X + (1-p) \frac{\text{Tr}(X)}{2^n} \mathbb{I}_{2^n}
$$
where $\mathbb{I}_{d}$ is ...
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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 $...
glS♦
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