PreprintarXiv licencearXiv
Provable circuit-level thresholds for non-abelian topological phases
Abstract
We provide an explicit scheme to realize a quantum memory in any 2D non-chiral topological order. For this, we construct syndrome extraction circuits based on the Turaev-Viro path integral as well as a classical algorithm for decoding on the fly. We prove that our scheme has a threshold under a local stochastic circuit-level noise model and discuss how to generalize it to implement topological logical gates.
Related
- Compactifications of Abelian Group Bundles and a Topological Halmos--von Neumann-type Theorem
- Torus Berry Data Determine All-Genus Abelian Topological Orders
- Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases
- Duality and Baire like properties in topological abelian groups
- A class of high-order discontinuous-Galerkin methods satisfying infinitely many entropy conditions with provable error estimates and strong convergence for general nonlinear conservation laws
BibTeX
@misc{ren2026provable,
title = {{Provable circuit-level thresholds for non-abelian topological phases}},
author = {Yuanjie Ren and Margarita Davydova and Shankar Balasubramanian and Andreas Bauer},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08488},
eprint = {2611.08488},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08488},
}
RIS
TY - UNPB
TI - Provable circuit-level thresholds for non-abelian topological phases
AU - Yuanjie Ren
AU - Margarita Davydova
AU - Shankar Balasubramanian
AU - Andreas Bauer
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08488
UR - https://arxiv.org/abs/2611.08488
AB - We provide an explicit scheme to realize a quantum memory in any 2D non-chiral topological order. For this, we construct syndrome extraction circuits based on the Turaev-Viro path integral as well as a classical algorithm for decoding on the fly. We prove that our scheme has a threshold under a local stochastic circuit-level noise model and discuss how to generalize it to implement topological logical gates.
ER -