Error thresholds for Abelian quantum double models: Increasing the bit-flip stability of topological quantum memory

Abstract

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 r/-level quantum systems (qudits) could provide advantages for quantum information processing. Among other merits, it has recently been shown that multilevel quantum systems can offer increased stability to external disturbances. 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 multilevel 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.

Ultracold polar molecules as qudits

“…Additionally, the time required to carry out gate operations can be reduced by a factor of ( ) d log 2 2 [16,20] if arbitrary transformations can be achieved in the d-dimensional space. Other advantages of using qudits for quantum computation are increased robustness [21][22][23] and improvements for quantum error-correcting codes [24][25][26][27][28][29][30].…”

Fast fault-tolerant decoder for qubit and qudit surface codes

“…For example, an integral part of many faulttolerant schemes is the distillation of magic states [10]-a procedure necessary to achieve universal computation-where generalization to higher dimensions has resulted in improved distillation thresholds and lower overheads in the number of qudit magic states [11][12][13]. Moreover, threshold investigations of the qudit toric code with noise-free syndrome measurements have shown that, for a standard independent noise model, the error correction threshold increases significantly with increasing qudit dimension [14][15][16], although we caution that it is difficult to fairly compare noise rates between systems of different dimensions. Although it is more challenging to realize qudit quantum systems experimentally, recent work has demonstrated the ability to coherently control and perform operations in single 16-dimensional atomic systems with high fidelity [17,18], with the implementation of high-fidelity multiqudit interactions still to be achieved.…”

Continuous error correction for Ising anyons

“…[25] to the continuous case. The "true" thresholds for Abelian models can often be assessed by finding the phase-transition in a related classical statistical mechanics model [30,47,48]. Whether something similar can be done for non-Abelian models remains an open problem.…”