  Charge noise remains the primary obstacle to the development of quantum
information technologies with semiconductor spin qubits. We use an exact
analytical calculation to determine the effects of quasistatic charge noise on
a ring of three equally spaced exchange-coupled quantum dots. We calculate the
disorder-averaged return probability from a specific initial state, and use it
to determine the coherence time T2* and show that it depends only on the
disorder strength and not the mean interaction strength. We also use a
perturbative approach to investigate other arrangements of three or four
qubits, finding that the return probability contains multiple oscillation
frequencies. These oscillations decay in a Gaussian manner, determined by
differences in energy levels of the Hamiltonian. We give quantitative values
for gate times resulting in several target fidelities. We find that the
decoherence time decreases with increasing number of qubits. Our work provides
useful analytical insight into the charge noise dynamics of coupled spin
qubits.
