Color codes [$200]

[Krastanov]

Color codes support for Quantum Clifford's ECC module

After Surface codes, color codes seem to be the most popular topological error correcting codes, and it would be nice to have them available for easy use in Quantum Clifford. Specifically, it would be nice to have built in functions to generate stabilizer tableaux for different color codes, as well as test different syndrome extraction techniques and decoders.

• As there are a few varieties of color codes, a first step to this functionality would be to implement some relevant hardcoded structures, so that a user could easily obtain color code stabilizer tableaux, which can then be combined with pre-existing generic syndrome extraction circuit functionality within QuantumClifford.jl.
• A second step would be to extend the above functionality to be able to generate color codes of arbitrary sizes based on user-inputed parameters.
• Outside of the scope of the bounty: A third step would then be to add color code specific syndrome extracting circuits as discussed in (for example Fig 2): https://arxiv.org/pdf/2312.08813
• Outside of the scope of the bounty: A fourth step would be to add decoders specific to the color codes, also discussed in the above paper.

Required skills: Knowledge of QuantumClifford, color codes, the quantum error correction pipeline, and error correction decoders (for step 4)

Reviewer: Stefan Krastanov

Duration: a month per step

Publication: In the next 2 years we plan to release a paper in a selective journal about this software. Contributing to this issue would deserve a co-authorship status on such a paper (if the contributor so desires)

Payout procedure:

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[Krastanov]

@amicciche ping as you expressed interest in this