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Shadow bootstrapping: Nearly minimal-setting pure-state tomography with shallow Clifford measurements — arXiv:2611.06073

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.06073
License (as archived): CC0-1.0
Archived: 2026-11-05T18:32:50.660Z
SHA-256 of the archived text: 794e5a2debd6e84e6b07700b5d4266066eb9fbecc462120f7bd5503df00035e0
Stable URL of this page: https://metraipolis.com/documento/dc_6ff0207c01e2

How to cite

Shadow bootstrapping: Nearly minimal-setting pure-state tomography with shallow Clifford measurements — arXiv:2611.06073 — arXiv (en), https://arxiv.org/abs/2611.06073 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_6ff0207c01e2 (Metraipolis archive dc_6ff0207c01e2, sha256 794e5a2debd6e84e6b07700b5d4266066eb9fbecc462120f7bd5503df00035e0)

BibTeX

@misc{dc6ff0207c01e2,
  title = {Shadow bootstrapping: Nearly minimal-setting pure-state tomography with shallow Clifford measurements — arXiv:2611.06073},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.06073},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_6ff0207c01e2; sha256 794e5a2debd6e84e6b07700b5d4266066eb9fbecc462120f7bd5503df00035e0},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.06073. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We present a pure-state tomography algorithm that uses a nearly minimal number of measurement settings while achieving optimal sample complexity with nonadaptive single-copy shallow Clifford measurements. For an arbitrary $n$-qubit pure state $|\psi\rangle \in \mathbb{C}^{d}$, where $d=2^n$, the algorithm uses $O(d/\epsilon)$ copies and $\widetilde{O}(1)$ measurement settings to output a state vector $|\hat{\psi}\rangle$ satisfying $1-|\langle\psi|\hat{\psi}\rangle|^2\le\epsilon$ with high probability. Each measurement is implemented by a Clifford circuit of depth $O(\log n)$. Reusing each measurement setting allows the data to be stored compactly as per-basis outcome histograms. Given these histograms, classical post-processing runs in $\widetilde{O}(d)$ time. Our key technique, \textit{shadow bootstrapping}, uses the current estimate to reduce the variance of subsequent residual estimation, enabling progressively more accurate reconstruction with only a constant number of new measurement settings per stage.

Tema degli esploratori: fisica e astronomia (elenco arXiv quant-ph, nuovi lavori del giorno).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2611.06073 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-05T18:22:49.018Z dalla pagina https://arxiv.org/list/quant-ph/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).