[SiteTypes] Add S2 operator for S=1 and update code style

[emstoudenmire]

This PR fixes #1501 by defining the "S2" (aka "S²") operator for the "S=1" SiteType. It also updates the code for "S=1" operator definitions to use the op matrices approach rather than the op! functions. A unit test was added for the "S2" operator.

[emstoudenmire]

Hm, when I rerun JuliaFormatter on the code it doesn't make any changes, yet it failed the Format Check. This also happened to me another time recently. I wonder if the formatting styles are out of sync between the CI and the code repo somehow? Or maybe these are just one-offs.

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 22.72727% with 17 lines in your changes missing coverage. Please review.

Project coverage is 60.84%. Comparing base (82cfd76) to head (98cc15a).
Report is 12 commits behind head on main.

❗ Current head 98cc15a differs from pull request most recent head 74a1d49

Please upload reports for the commit 74a1d49 to get more accurate results.

Files	Patch %	Lines
src/lib/SiteTypes/src/sitetypes/spinone.jl	22.72%	17 Missing ⚠️

❗ Your organization needs to install the Codecov GitHub app to enable full functionality.

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #1502       +/-   ##
===========================================
- Coverage   78.05%   60.84%   -17.21%     
===========================================
  Files         148      148               
  Lines        9679     9634       -45     
===========================================
- Hits         7555     5862     -1693     
- Misses       2124     3772     +1648     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[mtfishman]

What version of JuliaFormatter.jl do you have locally? Maybe you are using an older version locally.

The CI formatting suggestion looks correct to me:

julia> using JuliaFormatter

julia> format_text("1."; style=DefaultStyle())
"1.0"

julia> format_text("1."; style=BlueStyle())
"1.0"

julia> import Pkg; Pkg.status("JuliaFormatter")
Status `~/.julia/environments/v1.10/Project.toml`
  [98e50ef6] JuliaFormatter v1.0.56

See:

• https://domluna.github.io/JuliaFormatter.jl/stable/#trailing_zero
• https://domluna.github.io/JuliaFormatter.jl/stable/api/#JuliaFormatter.format_text-Tuple{AbstractString}
• https://github.com/JuliaDiff/BlueStyle?tab=readme-ov-file#numbers
• Begin to attempt to add trailing zeros to Float literals domluna/JuliaFormatter.jl#66

[emstoudenmire]

I resolved the formatter issue, thanks.

I didn't realize about the aliases – nice pattern.
I defined aliases for the spin operators and updated both spinone.jl and qubit.jl (underlying "S=1/2") to use these.
Also I made an alias for "SpinOne" -> "S=1" inside spinone.jl.

[emstoudenmire]

Of course one could envision many improvements to this system, like maybe a more unified way of handling spin operators since e.g. some of the aliases are repeated a bit, but I think this PR is a good "maintenance" sort of PR.

[mtfishman]

Yeah it would be good to step back and be a bit more systematic about the operator definitions code but that can be done in future work.

[mtfishman]

Thanks!