and incoherent error parameters together with the effective two-qubit interactions, whose combined action dominates the decoherence of quantum memory states. We find that a valid modeling of the dynamics of superconducting qubits requires one to properly account for coherent frequency shifts, caused by stochastic charge-parity fluctuations. We present a numerical approach that is scalable to tens of qubits, allowing us to simulate efficiently the dissipative dynamics of some large multiqubit states. Comparing our simulations to measurements of stabilizers dynamics of graph states realized experimentally with up to 12 qubits on a ring, we find that a very good agreement is achievable. Our approach allows us to probe nonlocal state characteristics that are inaccessible in the experiment. We show evidence for a significant improvement of the many-body state fidelity using dynamical decoupling sequences, mitigating the effect of charge-parity oscillations and two-qubit crosstalk.