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Single-shot state preparation threshold: rigorous theorem and statistical mechanical mapping — arXiv:2609.39965

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.39965
License (as archived): CC0-1.0
Archived: 2026-10-07T15:21:52.150Z
SHA-256 of the archived text: e35e4bc92bfa54b830b7f62d76333e43e3489dd8176f9e637c7ea2d7105f2526
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How to cite

Single-shot state preparation threshold: rigorous theorem and statistical mechanical mapping — arXiv:2609.39965 — arXiv (en), https://arxiv.org/abs/2609.39965 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f4d64c12866a (Metraipolis archive dc_f4d64c12866a, sha256 e35e4bc92bfa54b830b7f62d76333e43e3489dd8176f9e637c7ea2d7105f2526)

BibTeX

@misc{dcf4d64c12866a,
  title = {Single-shot state preparation threshold: rigorous theorem and statistical mechanical mapping — arXiv:2609.39965},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.39965},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f4d64c12866a; sha256 e35e4bc92bfa54b830b7f62d76333e43e3489dd8176f9e637c7ea2d7105f2526},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.39965. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Preparing logical codewords with a single round of noisy syndrome measurements can reduce the time overhead of fault-tolerant quantum computation. It remains unclear which structural properties of the code suffice to guarantee a threshold for single-shot state preparation. Here we prove that linear confinement suffices for a nonzero single-shot state-preparation threshold for CSS quantum low-density parity-check codes, in contrast to the common belief that soundness is necessary. When the distance is at least logarithmic, we prove that below nonzero local stochastic readout and data error thresholds, the logical error probability after a formal ideal final recovery is exponentially small and approaches zero when the code size approaches infinity. Under the stronger assumption of linear soundness, we show that the residual data error of the preparation protocol is local stochastic, directly allowing composition with other fault-tolerant gadgets. To investigate single-shot state-preparation threshold beyond the above assumptions, we further develop a statistical mechanical mapping that expresses the final logical error rate in terms of a classical partition function. We perform Monte Carlo simulations of this model for the three-dimensional toric code. The numerical results suggest that sublinear soundness can also support a single-shot state-preparation threshold.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-01 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.39965 — 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 2026-10-07T14:53:56.763Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).