Research Paper#Quantum Computing, Error Correction, Fracton Codes🔬 ResearchAnalyzed: Jan 3, 2026 19:28
Optimal Threshold and High Capacity of Fracton Codes
Published:Dec 28, 2025 11:36
•1 min read
•ArXiv
Analysis
This paper investigates the fault-tolerant properties of fracton codes, specifically the checkerboard code, a novel topological state of matter. It calculates the optimal code capacity, finding it to be the highest among known 3D codes and nearly saturating the theoretical limit. This suggests fracton codes are highly resilient quantum memory and validates duality techniques for analyzing complex quantum error-correcting codes.
Key Takeaways
- •Fracton codes, specifically the checkerboard code, exhibit high fault tolerance.
- •The checkerboard code achieves a high code capacity, approaching the theoretical limit.
- •Duality techniques are validated as useful for analyzing complex quantum error-correcting codes.
- •Haah's code also likely possesses a code capacity near the theoretical limit.
Reference
“The optimal code capacity of the checkerboard code is $p_{th} \simeq 0.108(2)$, the highest among known three-dimensional codes.”