  Current approaches for building quantum computing devices focus on two-level
quantum systems which nicely mimic the concept of a classical bit, albeit
enhanced with additional quantum properties. However, rather than artificially
limiting the number of states to two, the use of d-level quantum systems
(qudits) could provide advantages for quantum information processing. Among
other merits, it has recently been shown that multi-level quantum systems can
offer increased stability to external disturbances - a key problem in current
technologies. In this study we demonstrate that topological quantum memories
built from qudits, also known as abelian quantum double models, exhibit a
substantially increased resilience to noise. That is, even when taking into
account the multitude of errors possible for multi-level quantum systems,
topological quantum error correction codes employing qudits can sustain a
larger error rate than their two-level counterparts. In particular, we find
strong numerical evidence that the thresholds of these error-correction codes
are given by the hashing bound. Considering the significantly increased error
thresholds attained, this might well outweigh the added complexity of
engineering and controlling higher dimensional quantum systems.
