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 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.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 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.

arXiv:1406.5974Physical Review AApr 24, 201540 citations

Comparison of memory thresholds for planar qudit geometries

Jacob A. Marks, Tomas Jochym-O’Connor, Vlad Gheorghiu

We introduce and analyze a new type of decoding algorithm called general color clustering, based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under a generalized bit-flip error model, and is used to obtain the first memory threshold estimates for qudit 6-6-6 color codes. The proposed decoder is compared with similar decoding schemes for qudit surface codes as well as the current leading qubit decoders for both sets of codes. We find that, as with surface codes, clustering performs sub-optimally for qubit color codes, giving a threshold of compared to the obtained through surface projection decoding methods. However, the threshold rate increases by up to 112% for large qudit dimensions, plateauing around . All the analysis is performed using QTop , a new open-source software for simulating and visualizing topological quantum error correcting codes.We introduce and analyze a new type of decoding algorithm called general color clustering, based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under a generalized bit-flip error model, and is used to obtain the first memory threshold estimates for qudit 6-6-6 color codes. The proposed decoder is compared with similar decoding schemes for qudit surface codes as well as the current leading qubit decoders for both sets of codes. We find that, as with surface codes, clustering performs sub-optimally for qubit color codes, giving a threshold of compared to the obtained through surface projection decoding methods. However, the threshold rate increases by up to 112% for large qudit dimensions, plateauing around . All the analysis is performed using QTop , a new open-source software for simulating and visualizing topological quantum error correcting codes.

arXiv:1701.02335New Journal of PhysicsOct 16, 20179 citations

Topological quantum memory aÖ

Eric Dennis, Alexei Kitaev, Andrew J. Landahl +1 more

Jan 1, 20031 citation

Error threshold in topological quantum-computing models with color codes

Helmut G. Katzgraber, Héctor Bombín, Miguel Angel Martin-Delgado

Bulletin of the American Physical SocietyMar 19, 20090 citations

d

-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.