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Currently, the function expect_g(op::AbstractAdd, reg::MajoaranaReg) takes time O(n^3) because of the full matrix-matrix product. It may be possible to speed this up by not instantiating the full matrix form of op in the Majorana basis.

Currently only observables that are squares of Majoranas are supported in expect(). But generally, it is possible to calculate $⟨ψ|O|ψ⟩$ for arbitrary operators $O$ of the form $O = ∏_i L_i = ∏_i (∑_j O_{ij} γ_j)$ by calculating the pfaffian of the two-point matrix $M_{ij} = ⟨ψ|L_i L_j|ψ⟩$.

In order to get backward mode AD working I had to add the function :(*)(number::Real, reg::MajoranaReg) which is only a sensible operation if reg is a (co-)tangent register and not sensible if it is the primal register. This opens up potential incosistencies because we can do
expect(op, a * reg) but this doesn't satisfy expect(op, a * reg) == a * expect(op, reg).

One possible solution here is to add a TangentMajoranaReg type and only allow multiplication
with a scalar for that one.

I moved the docs from the (very long) README do docs/ and creating them locally via

pkg> activate docs/
julia> include("docs/make.jl")

works fine and the doctests pass. However, they do not get deployed online (or at least the link https://quantumbfs.github.io/FLOYao.jl/dev/) does not work yet.

@Roger-luo I am sure you know how to fix that 😀

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The title says it all. We probably want to be consistent with the Yao API here and return
complex numbers, even though the imaginary part should always be zero. At least with the observables that are supported so far.

Currently there is no function to generate random MajoranaRegs. Ideally, such a FLOYao.rand_state() function would generate states that are Haar randomly distributed in $O(2nq)$. I could either use

• RandomMatrices.rand(Haar(1), 2nq)
• use [this algorithm](https://en.wikipedia.org/wiki/Orthogonal_matrix#Randomization)
  to generate such Haar random matrices.