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Charge noise remains the primary obstacle to the development of quantuminformation technologies with semiconductor spin qubits. We use an exactanalytical calculation to determine the effects of quasistatic charge noise ona ring of three equally spaced exchange-coupled quantum dots. We calculate thedisorder-averaged return probability from a specific initial state, and use itto determine the coherence time T2* and show that it depends only on thedisorder strength and not the mean interaction strength. We also use aperturbative approach to investigate other arrangements of three or fourqubits, finding that the return probability contains multiple oscillationfrequencies. These oscillations decay in a Gaussian manner, determined bydifferences in energy levels of the Hamiltonian. We give quantitative valuesfor gate times resulting in several target fidelities. We find that thedecoherence time decreases with increasing number of qubits. Our work providesuseful analytical insight into the charge noise dynamics of coupled spinqubits.

Exact analytical treatment of multiqubit noisy dynamics in exchange-coupled semiconductor spin qubits