  Recent experimental studies have shown that the relaxation time, $T_1$, and
the dephasing time, $T_2$, of superconducting qubits fluctuate considerably
over time. Time-varying quantum channel (TVQC) models have been proposed in
order to consider the time varying nature of the parameters that define qubit
decoherence. This dynamic nature of quantum channels causes a degradation of
the performance of quantum error correction codes (QECC) that is portrayed as a
flattening of their error rate curves. In this article, we introduce the
concepts of quantum outage probability and quantum hashing outage probability
as asymptotically achievable error rates by a QECC with quantum rate $R_Q$
operating over a TVQC. We derive closed-form expressions for the family of
time-varying amplitude damping channels (TVAD) and study their behaviour for
different scenarios. We quantify the impact of time-variation as a function of
the relative variation of $T_1$ around its mean. We conclude that the
performance of QECCs is limited in many cases by the inherent fluctuations of
their decoherence parameters and corroborate that parameter stability is
crucial to maintain the excellent performance observed over static quantum
channels.
