Haah's cubic code using abelian group ℤ₃ˣ³ via Hecke's Group Algebra

[Fe-r-oz]

This PR aims to implement Haah's cubic code, a cousin of Generalized Bicycle code as mentioned in https://errorcorrectionzoo.org/c/generalized_bicycle.

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 83.02%. Comparing base (45e9f4d) to head (c96731f).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #388      +/-   ##
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+ Coverage   83.00%   83.02%   +0.01%     
==========================================
  Files          71       71              
  Lines        4560     4565       +5     
==========================================
+ Hits         3785     3790       +5     
  Misses        775      775              

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[Fe-r-oz]

I think this is ready for review, @Krastanov. Thanks!

Brief context: For GB codes , n%l+1 is used for GroupAlgebra (GA) indexing to indicate the cyclic nature for single cyclic group. This is same as doing n%dim(GA)+1. This works as here, we have a single cyclic group of order l, so total order is l which can be acquired using dim(GA).

In Haah cubic code case, the total order is l³, hence using n%dim(GA)+1 is appropriate since dim(GA) would give l³ because here, direct product of three cyclic groups ( total order = lxlxl) is the requirement. Also, The CI errors are unrelated to this PR.

Edit:

For large values of l, there are some crashes due to huge cubic lattice, GA with sparse representation is being worked on by Tommy here: thofma/Hecke.jl#1655. I will add this functionality once available.

[Krastanov]

Another great addition, thank you! I left in a few comments.

[Krastanov]

see also: bicycle_codes, generalized_bicycle_codes

[Fe-r-oz]

The CI is failing on master due to this:

QuantumClifford.jl/ext/QuantumCliffordHeckeExt/lifted_product.jl

Lines 253 to 256 in 45e9f4d

	julia> B = 𝜋^8 + 𝜋^14 + 𝜋^47;
	(108, 12)

This was fixed with the the see also.

Edit: It seems that theCI is not failing due to the extra spaces, I thought it would cause error when checking docstring.

[Krastanov]

The CI is failing on master due to this:

QuantumClifford.jl/ext/QuantumCliffordHeckeExt/lifted_product.jl

Lines 253 to 256 in 45e9f4d

	julia> B = 𝜋^8 + 𝜋^14 + 𝜋^47;
	(108, 12)

This was fixed with the the see also.

Edit: It seems that theCI is not failing due to the extra spaces, I thought it would cause error when checking docstring.

that fix is still nice to have!

I think it is failing because there are still a few spots with the old capitalization of the name of the code

[Krastanov]

marking as draft to make it easier for me to track what needs review

[Fe-r-oz]

The PR is ready for review. Thank you!

It was indeed the old capitalization in some places that was causing the CI errors.