Solovay-Kitaev Decomposition Algorithm

[obliviateandsurrender]

Context: Implements the Solovay-Kitaev decomposition algorithm using the description mentioned in arXiv:0505030

Description of the Change: This adds a Solovay-Kitaev decomposition for the Clifford+T workflow in the solovay_kitaev.py file.

1. sk_decomposition technique is the parent method, which takes in any single-qubit operator and uses its SU(2) representation for finding its decomposition in the specified basis up to a global phase via recursive implementation contained in _solovay_kitaev function.
2. _approximate_set method allows us to build an approximate set of Clifford sequences that are used in the base case return for the above _solovay_kitaev recursive call.
3. _group_commutator_decompose allows us to perform the group commutation decomposition and uses the recipe mentioned in Sec 4.1 arXiv:0505030.

Benefits: Should allow one to do the Clifford+T decomposition.

Possible Drawbacks: Better algorithms exist in the literature, specifically for decomposing rotation gates.

Related GitHub Issues:

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (d13cf3d) 99.65% compared to head (ba18503) 99.64%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4801      +/-   ##
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- Coverage   99.65%   99.64%   -0.02%     
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  Files         383      385       +2     
  Lines       34600    34460     -140     
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- Hits        34480    34337     -143     
- Misses        120      123       +3     

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[timmysilv]

🎉

[trbromley]

Thanks @obliviateandsurrender @timmysilv! My only remaining comments are related to the docs.

[timmysilv]

:')