Hello,

In a second-order Pauli-Z evolution circuit for the ZZ feature map with ϕ_{i} (x)=x_i and ϕ_{1,2} (x)=(π-x_1 ) (π-x_2 ) (Havlíček et. al., 2019), the circuit design represents these functions with specific gates. Specifically, ϕ_{i} (x) is implemented by the gate U1(2 * X[0]), and ϕ_{1,2} (x) is implemented by U1(2 *( π- X[0])* ( π- X[1])).

I have observed a multiplication by ‘2’ in these gate parameters when designed and implemented. I am curious about the rationale behind this factor ‘2’. Is it a constant factor, and why is it specifically ‘2’? Additionally, can this factor be any real number, and should it be the same for all wires in the circuit?

Thank you in advance!