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Hyperbolic Color Codes Reached Constant Rate and Polynomial Distance
The construction combines high-rate qLDPC scaling with color-code structure in dimensions four and above.
Summary
The construction combines high-rate qLDPC scaling with color-code structure in dimensions four and above.
Earlier hyperbolic color-code constructions reached at most logarithmic code distance. Building on arithmetic hyperbolic manifolds, this work constructs families with constant encoding rate and polynomial distance in even dimensions, with polynomial logical-qubit and distance scaling in the other covered cases. The paper derives explicit lower-bound exponents by dimension and code type. This is a mathematical construction and testbed for fault-tolerant protocols, not a hardware demonstration.
Why it matters
The construction combines high-rate qLDPC scaling with color-code structure in dimensions four and above.
Limits and context
- This is a mathematical construction and testbed for fault-tolerant protocols, not a hardware demonstration.
Key claims
The construction combines high-rate qLDPC scaling with color-code structure in dimensions four and above.
Qualification: This is a mathematical construction and testbed for fault-tolerant protocols, not a hardware demonstration.
Evidence: source-2026-09-16-019
Sources
- arXiv preprint 2609.16125arXiv · primary research
Corrections
No corrections have been recorded for this story.