Hi, Andrew! On page 123 equation C3 of the second paper, the symplectic matrix of two-mode sum gate is given as following:

$$\text{SUM}(\lambda) = \begin{pmatrix} 1 & 0 & -\frac{\lambda}{2} & +\frac{\lambda}{2} \\\ 0 & 1 & +\frac{\lambda}{2} & -\frac{\lambda}{2} \\\ +\frac{\lambda}{2} & +\frac{\lambda}{2} & 1 & 0 \\\ +\frac{\lambda}{2} & +\frac{\lambda}{2} & 0 & 1 \end{pmatrix}$$

So, is this okay :)

julia> basis = QuadPairBasis(2);

julia> lambda = 0.5;

julia> sum_unitary = sum_gate(basis, lambda)
GaussianUnitary for 2 modes.
  symplectic basis: QuadPairBasis
displacement: 4-element Vector{Float64}:
 0.0
 0.0
 0.0
 0.0
symplectic: 4×4 Matrix{Float64}:
 1.0   0.0   -0.25   0.25
 0.0   1.0    0.25  -0.25
 0.25  0.25   1.0    0.0
 0.25  0.25   0.0    1.0

And symbolic implementation :)

julia> using Symbolics

julia> @variables λ;

julia> sum_unitary_symbolic = sum_gate(basis, λ)
GaussianUnitary for 2 modes.
  symplectic basis: QuadPairBasis
displacement: 4-element Vector{Float64}:
 0.0
 0.0
 0.0
 0.0
symplectic: 4×4 Matrix{Num}:
     true         0  (-1//2)*λ   (1//2)*λ
        0      true   (1//2)*λ  (-1//2)*λ
 (1//2)*λ  (1//2)*λ       true          0
 (1//2)*λ  (1//2)*λ          0       true

Thank you for your help!

Implement two-mode summing unitary #38

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