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?

Filter by
Sorted by
Tagged with
3
votes
1answer
49 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)*...
2
votes
1answer
59 views

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)
3
votes
1answer
86 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 ...
7
votes
2answers
114 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 ...
4
votes
2answers
393 views

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 ...
6
votes
2answers
203 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 $...