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Achieving the limits of automorphism gates — arXiv:2609.19250

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19250
License (as archived): CC0-1.0
Archived: 2026-10-10T05:48:26.957Z
SHA-256 of the archived text: b935851b5a018fc35b8b727bee55e05c9e5cb991bd62f4bcc1827518d68696fb
Stable URL of this page: https://metraipolis.com/documento/dc_c6609ea41f4e

How to cite

Achieving the limits of automorphism gates — arXiv:2609.19250 — arXiv (en), https://arxiv.org/abs/2609.19250 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_c6609ea41f4e (Metraipolis archive dc_c6609ea41f4e, sha256 b935851b5a018fc35b8b727bee55e05c9e5cb991bd62f4bcc1827518d68696fb)

BibTeX

@misc{dcc6609ea41f4e,
  title = {Achieving the limits of automorphism gates — arXiv:2609.19250},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19250},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_c6609ea41f4e; sha256 b935851b5a018fc35b8b727bee55e05c9e5cb991bd62f4bcc1827518d68696fb},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19250. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Universal fault-tolerant quantum computing combines versatile but expensive operations with specialized but cheap ones. Its efficiency depends on how much computation can be pushed onto the cheap operations and on the size of the code needed to do so. Automorphism gates provide such cheap operations using only physical single-qubit Clifford gates and qubit permutations. Yet no general theory characterizes their maximum logical power or the minimum code size needed to attain it. We develop such a theory. For stabilizer codes encoding $k\geq3$ logical qubits, we show that the largest logical group attainable by automorphisms is generated by all addressable $S$ and $\mathrm{CX}$ gates, and we construct codes attaining it. While this group contains exponentially fewer gates than the full Clifford group, adding one suitable non-Clifford gate yields universality. We further classify the largest logical groups attainable using qubit permutations, physical single-qubit Cliffords, or both across general stabilizer and CSS codes, and derive refined bounds for self-dual CSS subclasses. Achieving the maximum-size logical group through automorphisms requires $n=\Theta(2^k)$ physical qubits. By contrast, all addressable diagonal Clifford gates, generated by $S$ and $\mathrm{CZ}$, require only $n=\Theta(k^2)$ physical qubits when implemented using physical single-qubit Cliffords alone. Both bounds are tight. This polynomial qubit cost extends beyond Cliffords to all addressable diagonal gates at any fixed level of the Clifford hierarchy, using physical single-qubit diagonal gates. Thus, for full addressability, the sharpest physical-qubit cost divide lies between diagonal and $\mathrm{CX}$-type gates, not between Clifford and non-Clifford gates.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-18 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.19250 — 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 2026-10-10T05:18:18.865Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).