Quantum

Junction Hook Errors in the Color Code

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 27/10/2026, 04:13:25 UTC.

Briefings

A new class of distance-reducing errors called junction hook errors was identified in the color code, occurring at logical operator junctions where data qubits of different colors meet. Unlike single-color malign hooks, these errors cannot accumulate on one logical operator, limiting their impact. Verification showed that for distances d=7,9,11, every non-corner plaquette admits a scheduled junction hook error combined with single data qubit faults, producing undetectable logical errors using d-1 faults. This finding explains why the circuit-level distance improved to d-floor((d+3)/6) rather than the spatially uniform d/2 distance.

Key points

• Junction hook errors occur at logical operator junctions where data qubits of different colors meet, reducing distance but not fitting the single-type anyon classification.
• For distances d=7,9,11, every non-corner plaquette admits a scheduled junction hook error combined with single data qubit faults, producing undetectable logical errors using d-1 faults.

Context

This research addresses color-dependent syndrome extraction schedules proposed to mitigate hook errors in the triangular color code. The study builds on prior work by Kishony and Fowler regarding distance-reducing errors by anyon type, identifying a new class of errors that do not fit existing classifications. The findings are based on arXiv preprints and represent a significant step in understanding circuit-level distance improvements.

Limitations

The evidence is limited to a single preprint (arXiv:2610.33347v1) and does not include experimental verification or broader application studies. The specific distances d=7,9,11 are verified for non-corner plaquettes, but the generalizability to other plaquette types or larger distances remains unverified. The source is preprint status, so the findings are subject to potential revision or correction.

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