Type promotion between MixedDestabilizer, Stabilizer and others, also used in ⊗

[Fe-r-oz]

With this fix, sm ⊗ S"X" from #260 will be added without any worry of StackOverflow error.

• The code is properly formatted and commented.
• Substantial new functionality is documented within the docs.
• All new functionality is tested.
• All of the automated tests on github pass.

P.S. Pondering about more tests for this.

Local Output w.r.t Task 4.

     Testing Running tests...
skipping gpu tests (set GPU_TESTS=true to test gpu)
Starting tests with 1 threads out of `Sys.CPU_THREADS = 4`...
[ Info: SetupBuildDirectory: setting up build directory.
[ Info: Doctest: running doctests.
[ Info: Skipped ExpandTemplates step (doctest only).
[ Info: Skipped CrossReferences step (doctest only).
[ Info: Skipped CheckDocument step (doctest only).
[ Info: Skipped Populate step (doctest only).
[ Info: Skipped RenderDocument step (doctest only).
WARNING: using LinearAlgebra.I in module QuantumClifford conflicts with an existing identifier.
Skipping Base.active_repl
Skipping Base.active_repl_backend
Test Summary: |   Pass   Total     Time
Package       | 285936  285936  7m19.9s
     Testing QuantumClifford tests passed 

[Fe-r-oz]

Tasks Completed:

• MixedDestabilizer ⊗ Stabilizer: md ⊗ S"X"
• Stabilizer ⊗ MixedDestabilizer: S"X" ⊗ md

[Fe-r-oz]

I think it is correct to say the resulting MixedDestabilizer resulting from md ⊗ S"X" should pass the mixed_destab_looks_good to ensure a consistent MixedDestabilizer. I have added tests for this to hold.

[Krastanov]

Half of this is on the correct path, but the other half presents complication we can avoid. Look into promote_rule if you would like to complete this PR.

[Fe-r-oz]

Thank you, promote_rule was very helpful. Addressed all of your comments.

I think the PR is ready for review.

P.S. Pardon for last 1 commit :( , applied further polishing.

[Krastanov]

There are some conceptual errors here about how to convert between different representations -- they are pretty fundamental to what each of the types actually means.

I also suggested a few simplifications.

[Krastanov]

I do not agree with many of these rules. A MixedStabilizer can not be converted to Stabilizer.

From special to general the conversions would be (missing a lot of type parameterizations):

Stabilizer, T<:Union{MixedStabilizer, Destabilizer, MixedDestabilizer} -> T
Destabilizer, MixedDestabilizer -> MixedDestabilizer
MixedStabilizer, MixedDestabilizer -> MixedDestabilizer

[Fe-r-oz]

Thank you, I agree with you. I will remove the nonsensical rules. Also, incorporate your last comment about not missing the type parameterizations.

tensor(MixedStab(...), S"X") causes stack overflow error if a user wants to cause it, so most of the nonsensical rules were to avoid the stack overflow errors. But yeah, they result in nonsense objects which I completely overlooked. Sorry about that.

[Fe-r-oz]

Thank you very much for special to general conversions #354 (comment), I have added them as instructed.

[Krastanov]

All of these converts can be implemented as something much simpler, e.g. convert(::T, x::AbstractStabilizer) where {T<:Type{S}, S<:AbstractStabilizer} = S(x) because we already have the constructors implemented. I probable screwed up some of the type syntax or names of types, but this is the rough idea.

[Fe-r-oz]

Thank you, my previous attempt was just so bad... I have removed all the nonsense and incorporated your comments. Specifically, I have revamped the promote rules based of your description. I had some complication using Base.convert(::Type{S}, x::AbstractStabilizer) where {S <: AbstractStabilizer} = S(x.tab) because the MixedStab and MixedDestab requires rank parameter as well. I simplified convert following the spirit of simplification as well.

Hopefully, this attempt is satisfactory and less awkward.

[Krastanov]

Thank you!