Crosstalk- and charge-noise-induced multiqubit decoherence in exchange-coupled quantum dot spin qubit arrays

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.