ZXW rewrite rules + Differentiation

[exAClior]

No description provided.

[codecov]

Codecov Report

Patch coverage: 79.17% and project coverage change: -0.43% ⚠️

Comparison is base (5161a51) 82.88% compared to head (6870623) 82.46%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #93      +/-   ##
==========================================
- Coverage   82.88%   82.46%   -0.43%     
==========================================
  Files          16       17       +1     
  Lines        2478     2902     +424     
==========================================
+ Hits         2054     2393     +339     
- Misses        424      509      +85     

Files Changed	Coverage Δ
src/ZXCalculus.jl	100.00% <ø> (ø)
src/zxw_diagram.jl	86.20% <ø> (ø)
src/parameter.jl	76.31% <45.45%> (-20.03%)	⬇️
src/zxw_rules.jl	73.44% <73.44%> (ø)
src/utils.jl	87.05% <94.15%> (+11.28%)	⬆️
src/to_eincode.jl	98.85% <100.00%> (+0.07%)	⬆️

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[exAClior]

Hello @ChenZhao44 , could you please take a look at my differentiation implementation while I continue to work on the integration part? I did minimal testing just in case I need to rewrite the entire thing.

[exAClior]

@ChenZhao44 Hi! I fixed and tested everything including differentiation, integration of two sites and four sites, variance calculation. Everything passed! Could you please take a look at it at your convenience? Thanks!

There are a few caveats for future user and future me.
1: If you found yourself missing a $\sqrt{2}$ in value sensitive calculation (derivative or integral), note the X spider used in ZXW Calculus related literature is actually a pink X spider, you need to adjust for $2^{(m+n-2)/2}$ where $m$ and $n$ are the number of in and out legs of the pink X spider
2: The ZXWDiagram representing the integral will be a factor of $1/2$ instead of $1/2\pi$ off from $\int_{0}^{2} \square d\theta$ where $\square$ represents the ZXDiagram calculating expectation value. This is because the spiders we used have rotation angles in units of $\pi$ not radians .

A merge of this PR should close #76 and #16

[exAClior]

Need to fix #97

[ChenZhao44]

Looks great now!