  We analyze in detail a procedure of entangling of two singlet-triplet
($S$-$T_{0}$) qubits operated in a regime when energy associated with the
magnetic field gradient, $\Delta B_{z}$, is an order of magnitude smaller than
the exchange energy, $J$, between singlet and triplet states [Shulman M. et
al., Science 336, 202 (2012)]. We have studied theoretically a single
$S$-$T_{0}$ qubit in free induction decay and spin echo experiments. We have
obtained analytical expressions for time dependence of components of its Bloch
vector for quasistatical fluctuations of $\Delta B_{z}$ and quasistatical or
dynamical $1/f^{\beta}$-type fluctuations of $J$. We have then considered the
impact of fluctuations of these parameters on the efficiency of the entangling
procedure which uses an Ising-type coupling between two $S$-$T_{0}$ qubits.
Particularly, we have obtained an analytical expression for evolution of two
qubits affected by $1/f^{\beta}$-type fluctuations of $J$. This expression
indicates the maximal level of entanglement that can be generated by performing
the entangling procedure. Our results deliver also an evidence that in the
above-mentioned experiment, the $S$-$T_{0}$ qubits were affected by
uncorrelated $1/f^{\beta}$ charge noises.
