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Clifford-hierarchy stabilizer formalism with applications to twisted quantum doubles — arXiv:2610.00464

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.00464
License (as archived): CC0-1.0
Archived: 2026-10-07T11:37:08.503Z
SHA-256 of the archived text: 2e026e6930778cdda1bca6c4e852e8a48a680ddf9bc4ed542340145f04987b36
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How to cite

Clifford-hierarchy stabilizer formalism with applications to twisted quantum doubles — arXiv:2610.00464 — arXiv (en), https://arxiv.org/abs/2610.00464 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d50d4eec516c (Metraipolis archive dc_d50d4eec516c, sha256 2e026e6930778cdda1bca6c4e852e8a48a680ddf9bc4ed542340145f04987b36)

BibTeX

@misc{dcd50d4eec516c,
  title = {Clifford-hierarchy stabilizer formalism with applications to twisted quantum doubles — arXiv:2610.00464},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.00464},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d50d4eec516c; sha256 2e026e6930778cdda1bca6c4e852e8a48a680ddf9bc4ed542340145f04987b36},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.00464. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Recent work has shown that quantum double models can be used to circumvent the Bravyi-Koenig bound. In particular, this is achieved through code-switching protocols in which non-Pauli stabilizer phases appear as intermediate codes. We introduce the $X\mathcal C^{(k)}_d$ stabilizer formalism, which generalizes the Pauli stabilizer formalism by combining Pauli-$X$ operators with diagonal operators drawn from a fixed level $k$ of the Clifford hierarchy on prime-dimensional qudits. This yields a natural class of beyond-Pauli stabilizer models, including many twisted quantum double phases. We classify a large class of these $X\mathcal C^{(k)}_d$ stabilizer states, showing that they are uniform superpositions over affine-linear subspaces with diagonal phases. In particular, when the stabilizers of a state require operators from level $k$ of the Clifford hierarchy, we show that the diagonal gates required to produce the phases in the wavefunction sit one level higher. We further show that every 2D twisted quantum double ${\cal D}^\omega(\mathbb{Z}_p^n)$ with $\omega$ a product of type-III cocycles and $p$ an odd prime admits a realization using only Clifford ($k=2$) stabilizers, and we conjecture that phases where $\omega$ contains a type-I or type-II cocycle require level-$p$ Clifford-hierarchy stabilizers for $p$-dimensional qudits. Finally, we demonstrate that a pair of qudit toric codes may be deterministically prepared in a logical magic state by measuring $X\mathcal C^{(k)}_d$ stabilizers. Together, these results provide a concrete stabilizer framework for topological codes beyond Pauli stabilizer models and their logical gates.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-02 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph) ; Strongly Correlated Electrons (cond-mat.str-el).
Pagina del lavoro: https://arxiv.org/abs/2610.00464 — 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 2026-10-07T11:19:01.625Z 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).