Is there a built-in Givens rotation gate (generated by XX + YY)?

[yliu7949]

Is there a built-in Givens rotation gate (generated by XX + YY)?

If not, how can I implement it myself to use it in the quantum circuit? Thanks.

[GiggleLiu]

XX+YY can not be the generator a rotation gate, because the generator is required to be reflexive and hermitian. For example the givens' rotation for |01> and |10> subspace can be represented as.

julia> op = (igate(2) + kron(X, X) + kron(Y, Y) + kron(Z, Z)) / 2
nqubits: 2
[scale: 0.5] +
   ├─ igate(2)
   ├─ kron
   │  ├─ 1=>X
   │  └─ 2=>X
   ├─ kron
   │  ├─ 1=>Y
   │  └─ 2=>Y
   └─ kron
      ├─ 1=>Z
      └─ 2=>Z


julia> mat(op ^ 2)   # reflexive requires op^2 = I
4×4 SparseMatrixCSC{ComplexF64, Int64} with 4 stored entries:
 1.0+0.0im      ⋅          ⋅          ⋅    
     ⋅      1.0+0.0im      ⋅          ⋅    
     ⋅          ⋅      1.0+0.0im      ⋅    
     ⋅          ⋅          ⋅      1.0+0.0im

julia> rot(op, 0.5)
rot(nqubits: 2
[scale: 0.5] +
   ├─ igate(2)
   ├─ kron
   │  ├─ 1=>X
   │  └─ 2=>X
   ├─ kron
   │  ├─ 1=>Y
   │  └─ 2=>Y
   └─ kron
      ├─ 1=>Z
      └─ 2=>Z
, 0.5)