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Time-varying quantum channels (TVQCs) have been proposed as a model to include fluctuations of the relaxation (T_{1}) and dephasing times (T_{2}). In previous works, realizations of multiqubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of T_{1} and T_{2} are block-to-block uncorrelated but qubit-wise perfectly correlated for the same block. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of five multiqubit quantum processors. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multiqubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the fast time-varying quantum channel (FTVQC). Furthermore, we lower-bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes when they operate over FTVQCs.