Allow custom axes when constructing operators, SymmetrySectors.jl and ITensorBase.jl extensions

[mtfishman]

This enables passing custom axes when constructing operators.

It also adds an ITensor extension for constructing ITensors when Index objects are passed as the axes.

This also adds an interface for specifying and customizing symmetries of axes/Index objects, similar to this old proposal: ITensor/ITensors.jl#522.

To-do:

• Add tests.
• Try to make Index(::SiteType) "just work" through a generic function (rangetype::Type{<:AbstractUnitRange}; kwargs...)(t::SiteType) = rangetype(AbstractUnitRange(t); kwargs...).
• Decide if multi-site operators like op("SWAP") should output n-dimensional arrays or matrices, this PR changes the behavior so that it reshapes to n-dimensional arrays, which is a bit annoying for dense arrays but makes sense for block sparse/symmetric tensors since reshaping is much less trivial in those cases.
• Look into how things work constructing ITensors for multi-site operators. Does the memory ordering match what is expected? The site indices may be reverse of what we want, since it is based on Julia's memory ordering convention.

Open to track elsewhere and fix in followup PRs:

• Fix "SWAP" gates so that sites of the output get swapped properly. The current code is correct if the sites are exactly the same, but with named dimensions and site of different sizes the code isn't correct. (Tracking in [BUG] Fix "SWAP" gates when sites aren't the same #20.)
• Consider making SiteType callable, similar to OpName and StateName, so that SiteType("S=1/2")() constructs the unit range AbstractUnitRange(SiteType("S=1/2")). (Tracking in [ENHANCEMENT] Consider making SiteType callable #18.)
• Diagonal operators are getting converted to dense with the current code design. (Tracking in [ENHANCEMENT] Diagonal operators are being converted to dense #19.)
• Constructing single-site states is hitting a bug in NamedDimsArrays since randn(2)[Index(2)] hits an ambiguity error. (Tracking in [BUG] randn(2)[Index(2)] is broken ITensorBase.jl#25.)
• When the axes are graded, currently the code constructs block dense arrays rather than block sparse arrays. We'll want to special getindex(::AbstractArray, ::AbstractGradedUnitRange...). (Tracking in [BUG] Issues slicing dense arrays by graded unit ranges GradedUnitRanges.jl#9.)
• randn(2, 2)[r, dual(r)] where r isa AbstractGradedUnitRange drops the dual information. (Tracking in [BUG] Issues slicing dense arrays by graded unit ranges GradedUnitRanges.jl#9.)
• There is an issue converting BitArrays to block arrays and ITensors when the axes are graded (probably will be fixed when the above issue is fixed). (Tracking in [BUG] Issues slicing dense arrays by graded unit ranges GradedUnitRanges.jl#9.)

[codecov]

Codecov Report

Attention: Patch coverage is 71.20000% with 36 lines in your changes missing coverage. Please review.

Project coverage is 68.65%. Comparing base (3df5640) to head (b36566f).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
...xt/QuantumOperatorDefinitionsSymmetrySectorsExt.jl	52.63%	18 Missing ⚠️
src/sitetype.jl	60.52%	15 Missing ⚠️
src/state.jl	71.42%	2 Missing ⚠️
src/op.jl	96.77%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main      #17       +/-   ##
===========================================
+ Coverage   28.20%   68.65%   +40.45%     
===========================================
  Files          11       13        +2     
  Lines         429      536      +107     
===========================================
+ Hits          121      368      +247     
+ Misses        308      168      -140     

Flag	Coverage Δ
docs	28.62% <31.96%> (+0.42%)	⬆️

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[mtfishman]

There are a number of open issues to resolve that I came across while working on this, mostly related to the interaction of BlockSparseArrays.jl, GradedUnitRanges.jl, and NamedDimsArrays.jl/ITensorBase.jl (so they need to be fixed in those packages), which are listed above and I raised issues in appropriate places for them. This PR already makes a lot of progress towards constructing abelian symmetric states and operators as ITensors, so I will merge this and work on those in followup PRs.