We give a shadow tomography algorithm that uses $O(\log(m) \log(m/\delta) / \varepsilon^2)$ copies of the input state. Specifically, given a quantum state $\rho$ and observables $O_1,\ldots,O_m$, the algorithm outputs estimates of $\mathrm{tr}(O_i\rho)$ for all $i\in[m]$ that are all accurate to within $\pm\varepsilon$...
Sabee Grewal, Angelos Pelecanos, Jack Spilecki et al.· 0 citations
The key to the proof is a new framework for quantifying post-measurement damage, based on the quantum Efron-Stein decomposition, which improves all three exponents even in the Offline Shadow Tomography setting.
Si-Tan Chen, R. O'Donnell, Angelos Pelecanos et al.· arXiv.org· 2 citations· ⚡1
We give an algorithm which, given $n = O(d^2 \cdot (\log\log(d)/\log(d))^2)$ copies of $\rho$, estimates the eigenvalues of $\rho$ to constant error in total variation distance. Thus, we can learn the eigenvalues of a quantum state with fewer copies than the $\Theta(d^2)$ needed to run full state tomography. This is th...
Angelos Pelecanos, Jack Spilecki, Ewin Tang et al.· arXiv.org· 5 citations· ⚡5
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