Add basic benchmarking workflow, create benchmark/ folder with bench script

[starsfordummies]

Ideally this should create some benchmark data in dev/bench/data.js in the gh-pages branch, as well as an accompanying index.html - I have an updated index.html as well but I don't know how to make it such that the pr puts it in the gh-pages folder...

the html file to put in gh-pages should be https://github.com/starsfordummies/testing_livebench/blob/gh-pages/dev/bench/index3.html

More info on the thing in https://github.com/marketplace/actions/continuous-benchmark

[mofeing]

yeah, don't worry. we can later add it to the gh-pages (although i think we need an automated way).

let's start by adding some benchmarks. @starsfordummies @jofrevalles @Todorbsc what do you think about benchmarking the following?

• contraction of 2 Tensors (matmul) for Float64 & ComplexF64. at least 3 different sizes (small, mid & large).
• contraction of 2 Tensors (more complex pattern) with the same variations.
• MPS overlap for different number of sites (L=10,=30,=60) and maximum bond dimensions
  • for L=10, use 2,32
  • for L=30, use 2,128,1024
  • for L=60, use 128,1024
• MPS canonization from NonCanonical to Canonical, from NonCanonical to MixedCanonical and from MixedCanonical to MixedCanonical in another site
  • yet to decide the benchmark space

we can benchmark more stuff in the future, but let's start with the following which are key to us right now

@starsfordummies i'm changing this to a draft PR because it's not yet ready to merge

[jofrevalles]

Hey @mofeing @starsfordummies @Todorbsc, I will design some benchmarks for this and let you know. Is this okay?

[mofeing]

@jofrevalles that sounds great! i would say that feel free to push to this PR so we can see the result