Error Thresholds for Abelian Quantum Double Models: Increasing the bit-flip Stability of Topological Quantum Memory

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.