  Many physical systems considered promising qubit candidates are not, in fact,
two-level systems. Such systems can leak out of the preferred computational
states, leading to errors on any qubits that interact with leaked qubits.
Without specific methods of dealing with leakage, long-lived leakage can lead
to time-correlated errors. We study the impact of such time-correlated errors
on topological quantum error correction codes, which are considered highly
practical codes, using the repetition code as a representative case study. We
show that, under physically reasonable assumptions, a threshold error rate
still exists, however performance is significantly degraded. We then describe
simple additional quantum circuitry that, when included in the error detection
cycle, restores performance to acceptable levels.
