Trotter approximation
To first order Trotter approximation we have
$$
\begin{align}
\tag{18}
\vert\Psi(\theta)\rangle
&\approx\prod_{ia}\exp\left\{\frac{i}{2}t_i^a\left(X_aY_i-Y_aX_i\right)\right\}\vert\Phi\rangle
\\
&\equiv
\prod_{ia}A_{ia}\vert\Phi\rangle.
\tag{19}
\end{align}
$$