Algebric prerequisites for Clifford+T decompositions

[obliviateandsurrender]

Context: This introduces and provides some algebraic prerequisites necessary for number-theoretic Clifford-T decomposition methods.

Description of the Change:

1. Adds Z[√2] (ring of quadratic integers with radicand 2)
2. Z[ω] (ring of cyclotomic integers of degree 8).
3. Adds matrices for Dyadic/SO3 descriptions.
4. Normal form conversion rules.
5. Tests for verify ordering.

Benefits:

Possible Drawbacks:

Related GitHub Issues:

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit doc/releases/changelog-dev.md with:

• A one-to-two sentence description of the change. You may include a small working example for new features.
• A link back to this PR.
• Your name (or GitHub username) in the contributors section.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.67%. Comparing base (549a288) to head (86dbf59).
Report is 2 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff            @@
##           master    #7588    +/-   ##
========================================
  Coverage   99.67%   99.67%            
========================================
  Files         532      534     +2     
  Lines       52374    52732   +358     
========================================
+ Hits        52204    52562   +358     
  Misses        170      170            

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[willjmax]

Here are some comments for the rings file. I'll take a look at normal forms later today.

[willjmax]

The code looks good, mostly just questions about how the algorithm works.

[willjmax]

Just a few more minor comments. Should be able to approve when they are addressed.

[willjmax]

Maybe give an example of the conversion for clarity.

[willjmax]

Almost there

[willjmax]

LGTM 🎉