Year: 2026
Type: preprint
Abstract: We study exact recovery for non-Abelian topological surface codes based on the quantum double $D(G)$ of any finite group $G$. We determine an orthogonal error basis, that is comprised of group multiplication and irreducible representation operators. Whenever the errors are supported on closed loops on the lattice or dual lattice, there is a redundancy in the basis, due to stabilizers. To remedy this, we introduce a gauge-fixing that results in a complete and orthogonal error basis on the code space. Assuming as input predetermined, neutral correctable error clusters, we construct charge and flux transfer circuits that move the errors onto ancillas that then get projected out. This is an exact and deterministic recovery protocol, applicable to surface codes for any finite, in particular non-Abelian, group $G$.
Source: arXiv (Cornell University)
Institutions: University of Oxford, Stony Brook University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: UK Research and Innovation
OpenAlex ID: W7220411981