embed for single-qubit and two-qubit symbolic Clifford Operators

[Fe-r-oz]

The PR #413 revealed to us that we don't have embed for single-qubit dense/symbolic Clifford Operator or two-qubit dense/symbolic Clifford Operator. Thus, this PR attemps to define embed for single-qubit Clifford Operator, thereby addressing a chunk of #151

Edit:

I think is is straightforward as we have already defined implicit embed as CliffordOperator(sCNOT(1, 2), 4) for instance!

julia> embed(5, (2,3), sCNOT)
X₁ ⟼ + X____
X₂ ⟼ + _XX__
X₃ ⟼ + __X__
X₄ ⟼ + ___X_
X₅ ⟼ + ____X
Z₁ ⟼ + Z____
Z₂ ⟼ + _Z___
Z₃ ⟼ + _ZZ__
Z₄ ⟼ + ___Z_
Z₅ ⟼ + ____Z

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 82.95%. Comparing base (c3546cd) to head (c940f2f).
Report is 1 commits behind head on master.

Additional details and impacted files

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  Coverage   82.94%   82.95%           
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  Files          70       70           
  Lines        4557     4559    +2     
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+ Hits         3780     3782    +2     
  Misses        777      777           

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[Fe-r-oz]

The PR is ready for review. Thank you!

[Krastanov]

Thanks for looking into this. Do we need an embed for these though? They already work fine on arbitrary number of qubits, i.e. they are already implicitly embedded. You can run apply!(stab, sCNOT(1,2)) on any size stab (if anything, an embed here would make thinks slower). You can not do that with apply!(stab, tCNOT) so an embed is needed.

I guess adding this functionality makes sense just for completeness, but there should be a warning in the docstring that this is a bad way to do it.

Also, it seems there is a single docstring for one of the methods that includes what is supposed to be a docstring for the other method. This should be two separate docstrings (if they are method dosctrings).

Lastly, the single-qubit embed should still permit one-tuples as argument types for i to be consistent with the rest of the embed methods

[Krastanov]

also, new functionality like this needs tests

[Fe-r-oz]

Thank you for your comments.

Do we need an embed for these though?

Actually, I considered closing this PR since the embedding is already handled implicitly. While it’s worth exploring alternative approaches while looking into #151, the final outcome here doesn’t offer much added value.

Instead of adding code that SLOW DOWN performance || is a BAD way to do things || might introduce redundant checks, we can simply update the documentation to clarify that the embedding is implicitly supported.

This also seems like an inefficient use of your valuable review time.

So, let's just close it :)