Validate and add docs for Gaussian objects containing symbolic variables

[apkille]

See qojulia/QuantumOpticsBase.jl#184 for a discussion. Symbolic variables from Symbolics.jl actually integrate quite nicely with Gabs:

julia> using Symbolics

julia> @variables r θ τ
3-element Vector{Num}:
 r
 θ
 τ

julia> b = QuadBlockBasis(2); st = eprstate(b, r, θ); op = beamsplitter(b, τ);

julia> newst = ptrace(op * st, 1)
GaussianState for 1 mode.
  symplectic basis: QuadBlockBasis
mean: 2-element Vector{Num}:
 0
 0
covariance: 2×2 Matrix{Num}:
 (0.5cosh(2r)*sqrt(1 - τ) - 0.5cos(θ)*sinh(2r)*sqrt(τ))*sqrt(1 - τ) + (0.5sqrt(τ)*cosh(2r) - 0.5cos(θ)*sinh(2r)*sqrt(1 - τ))*sqrt(τ)  …                                                                                                 -sinh(2r)*sin(θ)*sqrt(τ)*sqrt(1 - τ)
                                                                                                -sinh(2r)*sin(θ)*sqrt(τ)*sqrt(1 - τ)     (0.5cosh(2r)*sqrt(1 - τ) + 0.5cos(θ)*sinh(2r)*sqrt(τ))*sqrt(1 - τ) + (0.5sqrt(τ)*cosh(2r) + 0.5cos(θ)*sinh(2r)*sqrt(1 - τ))*sqrt(τ)

julia> using Latexify

julia> latexify(newst.covar)
L"\begin{equation}
\left[
\begin{array}{cc}
\left( 0.5 \cosh\left( 2 r \right) \sqrt{1 - \tau} - 0.5 \cos\left( \theta \right) \sinh\left( 2 r \right) \sqrt{\tau} \right) \sqrt{1 - \tau} + \left( 0.5 \sqrt{\tau} \cosh\left( 2 r \right) - 0.5 \cos\left( \theta \right) \sinh\left( 2 r \right) \sqrt{1 - \tau} \right) \sqrt{\tau} &  - \sinh\left( 2 r \right) \sin\left( \theta \right) \sqrt{\tau} \sqrt{1 - \tau} \\
 - \sinh\left( 2 r \right) \sin\left( \theta \right) \sqrt{\tau} \sqrt{1 - \tau} & \left( 0.5 \cosh\left( 2 r \right) \sqrt{1 - \tau} + 0.5 \cos\left( \theta \right) \sinh\left( 2 r \right) \sqrt{\tau} \right) \sqrt{1 - \tau} + \left( 0.5 \sqrt{\tau} \cosh\left( 2 r \right) + 0.5 \cos\left( \theta \right) \sinh\left( 2 r \right) \sqrt{1 - \tau} \right) \sqrt{\tau} \\
\end{array}
\right]
\end{equation}
"

$$\begin{equation} \left[ \begin{array}{cc} \left( 0.5 \cosh\left( 2 r \right) \sqrt{1 - \tau} - 0.5 \cos\left( \theta \right) \sinh\left( 2 r \right) \sqrt{\tau} \right) \sqrt{1 - \tau} + \left( 0.5 \sqrt{\tau} \cosh\left( 2 r \right) - 0.5 \cos\left( \theta \right) \sinh\left( 2 r \right) \sqrt{1 - \tau} \right) \sqrt{\tau} & - \sinh\left( 2 r \right) \sin\left( \theta \right) \sqrt{\tau} \sqrt{1 - \tau} \\\ - \sinh\left( 2 r \right) \sin\left( \theta \right) \sqrt{\tau} \sqrt{1 - \tau} & \left( 0.5 \cosh\left( 2 r \right) \sqrt{1 - \tau} + 0.5 \cos\left( \theta \right) \sinh\left( 2 r \right) \sqrt{\tau} \right) \sqrt{1 - \tau} + \left( 0.5 \sqrt{\tau} \cosh\left( 2 r \right) + 0.5 \cos\left( \theta \right) \sinh\left( 2 r \right) \sqrt{1 - \tau} \right) \sqrt{\tau} \\\ \end{array} \right] \end{equation}$$

So it would be great to make these features accessible in the tutorials section of the documentation, and add tests for them so they don't break in the future.

[Fe-r-oz]

Following the completing of #44, the TODOs are:

• Gaussian unitaries: Validate and add docs for symbolic Gaussian unitaries #46
• channels
• application products onto Gaussian states

I have submitted a basic attempt for TODO 1 at #46 :) Thank you so much for support and help in reviewing the PRs!