Metraipolis › archive › dc_febbb23511cf

Improved Transversal Non-Clifford Gates from Cup Products — arXiv:2609.27801

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.27801
License (as archived): CC0-1.0
Archived: 2026-10-08T12:12:08.693Z
SHA-256 of the archived text: 70248a908de6c58fb82af7e35cb0389bc3bb6b23ee19f30cc6f8984b6c308d0c
Stable URL of this page: https://metraipolis.com/documento/dc_febbb23511cf

How to cite

Improved Transversal Non-Clifford Gates from Cup Products — arXiv:2609.27801 — arXiv (en), https://arxiv.org/abs/2609.27801 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_febbb23511cf (Metraipolis archive dc_febbb23511cf, sha256 70248a908de6c58fb82af7e35cb0389bc3bb6b23ee19f30cc6f8984b6c308d0c)

BibTeX

@misc{dcfebbb23511cf,
  title = {Improved Transversal Non-Clifford Gates from Cup Products — arXiv:2609.27801},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.27801},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_febbb23511cf; sha256 70248a908de6c58fb82af7e35cb0389bc3bb6b23ee19f30cc6f8984b6c308d0c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.27801. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

It is a major challenge in quantum fault-tolerance to obtain low-overhead protocols for performing non-Clifford gates. In this vein, we construct quantum codes with low-weight stabilizers that support transversal (i.e. low-depth) implementations of the non-Clifford $C^{r-1}Z$ gate, for every constant $r\geq 3$. In particular, we obtain length-$n$ quantum LDPC codes (with constant-weight stabilizers) of polynomial distance $d\geq n^{(1-\epsilon)/r}$ supporting transversal $C^{r-1}Z$ gates on a close-to-linear number $k\geq n^{1-\epsilon}$ of disjoint tuples of logical qubits, for arbitrarily small $\epsilon>0$. Our construction is the first with constant-weight stabilizers that obtains $dk\gg n$, and as a consequence achieves arbitrarily small magic state overhead exponent $\gamma=\log(n/k)/\log(d)>0$. Comparable prior constructions instead required at least polylogarithmic stabilizer weight. We also show how to obtain linearly many $k=\Omega(n)$ logical $C^{r-1}Z$ gates, though with stabilizer weight and physical circuit depth $n^\epsilon$. We show that our transversal gates also support addressing (i.e. targeting) of specific logical qubits. To obtain our codes, we develop a general transformation based on cup products that maps classical codes satisfying a multiplication property to quantum codes with transversal $C^{r-1}Z$. We apply this transformation to a new family of classical Tanner codes that we construct from punctured tensor products of algebraic codes.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-24 in math.IT).
Categorie arXiv: Quantum Physics (quant-ph) ; Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2609.27801 — 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 2026-10-08T12:10:03.948Z dalla pagina https://arxiv.org/catchup/math.IT/2026-09-24?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).