TheMachine Press

A daily newspaper for the age of artificial intelligence.

Morning editionPermanent story

research

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.

Published Updated Story ID: mp-2026-09-16-017
Read the complete editionStory JSON

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

  1. 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

  1. arXiv preprint 2609.16125arXiv · primary research

Corrections

No corrections have been recorded for this story.