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I am a beginner in topological quantum codes and have been interested in quantum color codes recently. The 2-D quantum color codes have a very clear physical picture and can check stabilizers locally. However, I have two separate questions regarding them that I haven't found the answers in the literature so far.

  1. How did people come up with the idea of quantum color codes? Is there any inspiration from practical physical systems?
  2. What is the key advantage of quantum color codes? From this page, the code distance $d$ only scales logarithmically with $n$ (code size), a lot of qLDPC codes have better code distance scaling. So I guess the code rate is not an advantage for quantum color codes.
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Partial answer:

  1. Color codes require only local connectivity.
  2. Color codes are older than the recent practical QLDPC examples.
  3. In 2D color codes enable implementing the full logical Clifford group transversally, and in 3D, using methods of gauge-fixing, color codes enable a transversal, universal set of gates.
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