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Adaptivity is all you need: Optimal stabilizer learning using just single-copy measurements — arXiv:2610.02031

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.02031
License (as archived): CC0-1.0
Archived: 2026-10-07T11:38:19.570Z
SHA-256 of the archived text: 839153ece466a945abc9374d1a947a0ced95001953c96ba4574be50ba45b5701
Stable URL of this page: https://metraipolis.com/documento/dc_22abb79d60da

How to cite

Adaptivity is all you need: Optimal stabilizer learning using just single-copy measurements — arXiv:2610.02031 — arXiv (en), https://arxiv.org/abs/2610.02031 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_22abb79d60da (Metraipolis archive dc_22abb79d60da, sha256 839153ece466a945abc9374d1a947a0ced95001953c96ba4574be50ba45b5701)

BibTeX

@misc{dc22abb79d60da,
  title = {Adaptivity is all you need: Optimal stabilizer learning using just single-copy measurements — arXiv:2610.02031},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.02031},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_22abb79d60da; sha256 839153ece466a945abc9374d1a947a0ced95001953c96ba4574be50ba45b5701},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.02031. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Stabilizer states are central to quantum computing, underlying quantum error correction, benchmarking, and efficient classical simulation. Yet their learnability exhibits a striking gap: an $n$-qubit stabilizer state can be learned from $\Theta(n)$ copies using two-copy Bell measurements, whereas non-adaptive single-copy measurements require $\Omega(n^2)$ copies. Here we show that adaptivity completely closes this gap. We give a polynomial-time adaptive algorithm that learns an arbitrary $n$-qubit stabilizer state from $\Theta(n)$ single-copy Clifford measurements, matching the optimal sample complexity of Bell sampling without any multi-copy measurements. The same ideas yield a sample-optimal single-copy tolerant tester and, with $k$ qubits of quantum memory, the optimal testing tradeoff $\Theta(n-k+1/\varepsilon)$ at infidelity $\varepsilon$. Finally, we show that this adaptive mechanism extends beyond exact stabilizer states: states of stabilizer nullity at most $r$, including states prepared by Clifford circuits with a bounded number of $T$ gates, can be learned using $O(n2^{r})$ single-copy measurements.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-02 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.02031 — 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 2026-10-07T11:19:01.736Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).