How should one choose the distribution of the real parameters $a,b$ in the Hamiltonian $H(a,b) = a \sigma_x + b \sigma_y$ so that the resulting unitary operation $e^{-iH(a,b)t}$ (for a fixed $t$) approximates a Haar-random distribution?
I’m familiar with generating Haar-random unitaries in matrix form, but I’m unsure how to translate this into the Hamiltonian framework as described above.
