  We determine the interqubit crosstalk- and charge-noise-induced decoherence
time $T_2^\ast$ for a system of $L$ exchange-coupled electronic spin qubits in
arrays of size $L=3$--$14$ for a number of different multiqubit geometries by
directly calculating the return probability. We compare the behavior of the
return probability to other quantities, namely, the average spin, the Hamming
distance, and the entanglement entropy. In all cases, we use a starting state
with alternating spins, $\left |\Psi_0\right >=\left
|\downarrow\uparrow\downarrow\cdots\right >$. We show that a power law
behavior, $T_2^\ast\propto L^{-\gamma}$, is a good fit to the results for the
chain and ring geometries as a function of the number of qubits, and provide
numerical results for the exponent $\gamma$. We find that $T_2^\ast$ depends
crucially on the multiqubit geometry of the system. We also calculate the
expectation value of one of the spins, the Hamming distance, and the
entanglement entropy and show that they are good proxies for the return
probability for measuring $T_2^\ast$. A key finding is that $T_2^\ast$
decreases with increasing $L$. We also demonstrate that these results may be
understood in terms of perturbation theory and its breakdown.
