Quantum Computing, Qiskit, General U3 Gate, Controlled U3 Gate, Tutorial.
second equation: Using Euler’s formula, we can write it as: Since we have only imaginary part on the RHS, LHS has to match up. So, (𝜙+𝜆) has to be a value that gives 0 for cos and 1 for sin. i.e. (𝜙+𝜆)=3𝜋/2 (because cos(3𝜋/2)=0 and sin(3𝜋/2)=1) This gives us several possibilities for both 𝜙 and 𝜆: