Decoding non-Abelian topological quantum memories

Abstract

The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However the question of how to obtain and process information about what errors have occurred in order to negate their effects has not yet been considered. This is in stark contrast with quantum computation proposals for Abelian anyons, for which decoding algorithms have been tailor-made for many topological error-correcting codes and error models. Here we address this issue by considering the properties of non-Abelian error correction in general. We also choose a specific anyon model and error model to probe the problem in more detail. The anyon model is the charge submodel of $D(S_3)$. This shares many properties with important models such as the Fibonacci anyons, making our method applicable in general. The error model is a straightforward generalization of those used in the case of Abelian anyons for initial benchmarking of error correction methods. It is found that error correction is possible under a threshold value of $7\%$ for the total probability of an error on each physical spin. This is remarkably comparable with the thresholds for Abelian models.

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Cited by in corpus (31)

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• Majorana braiding with thermal noise
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• Fault-Tolerant Quantum Error Correction for non-Abelian Anyons
• Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
• Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment
• Monte Carlo studies of the properties of the Majorana quantum error correction code: is self-correction possible during braiding?
• A simple decoder for topological codes
• Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code
• Conservation laws and quantum error correction: towards a generalised matching decoder
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• Anyons are not energy eigenspaces of quantum double Hamiltonians
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• Simulation of braiding anyons using Matrix Product States
• Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
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• Stabilizing Non-Abelian Topological Order against Heralded Noise via Local Lindbladian Dynamics
• Quantum Lego and XP Stabilizer Codes
• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
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