Color code off-the-hook: avoiding hook errors with a single auxiliary per plaquette

Quantum Physics [Submitted on 30 Mar 2026] Color code off-the-hook: avoiding hook errors with a single auxiliary per plaquette Gilad Kishony, Austin Fowler Syndrome extraction in the planar color code is complicated by high weight stabilizers and hook errors that can reduce the circuit-level distance. With a single auxiliary qubit per plaquette, any spatially uniform circuit halves the circuit-level distance. We propose a single-auxiliary syndrome extraction circuit with color-dependent gate schedules that avoids all malign hook errors in the bulk, thereby preserving the full circuit-level distance. The circuit has minimal depth: all stabilizers of the same Pauli type are measured in parallel in six time steps. Furthermore, this schedule can be readily applied to the XYZ color code circuit, yielding an improved temporal distance. We find that at the boundary, no single hook error alone reduces the distance; instead, only certain combinations of hook errors do, which we call fractional hook errors. We demonstrate through Monte Carlo simulations over a range of circuit-level noise models and physical error rates that our circuit outperforms the previous state of the art. Comments: 6 pages, 3 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.28852 [quant-ph]   (or arXiv:2603.28852v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.28852 Focus to learn more Submission history From: Gilad Kishony [view email] [v1] Mon, 30 Mar 2026 18:00:01 UTC (195 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)