add package benchmarks

[Omar-Elrefaei]

This is a draft for benchmarks as discussed here #64.

So far I covered

1. time to import, latency
2. simple object instantiations
3. arithmetic operations
4. linear algebra
5. symbolic manipulation (expand, simplify)
6. expressing in optics/clifford backend

Please check if I missed any major features.

If there is any real usage notebook you'd like me to extract usages from I'd be happy to.
Also if you can hint me at specific directions of what a "hot loop" would look like, I could stress test that use case. I'm just not sure, for example, whether multiplication of hundreds of kets or ops is relevant or too contrived.

[Omar-Elrefaei]

Ping because this is a draft @Krastanov

[Krastanov]

This looks great! Thank you for spending time on it!

The only other thing that would be valuable to include is something that tests issues related to the fact that we are not using abstract data types (like Unityper, SumTypes, Expronicon, or Moshi). Because of the lack of this feature, manipulating large trees is actually somewhat expensive and it would be valuable to keep track of that expense.

So a holistic benchmark for that can look something like:

function make_large_tree_with_plenty_of_reallocations(layers)
    expr_op = identity
    expr_ket = X1
    for _ in 1:layers
        expr_op = rand([X,Y,Z,H,...])+rand([...])*expr_op
        expr_ket = expr_op*expr_ket + rand([X1,X2,Z1,Z2,...])
    end
    return expr_op, expr_ket
end


SUITE["large_tree"]["construct"]["10_layers"] = make_large_tree_with_plenty_of_reallocations(10)

We are not including tensor products here or superoperators, but that is probably fine until we invest time in actually using abstract data types.