Cellular automaton decoders for topological quantum codes with noisy measurements and beyond

Michael Vasmer,Dan E Browne,Aleksander Kubica

doi:10.1038/s41598-021-81138-2

Michael Vasmer, Dan E Browne + Show 1 more

Open Access

https://doi.org/10.1038/s41598-021-81138-2

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Abstract

We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, however, we focus on the three-dimensional toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We also numerically benchmark the performance of the decoder in the setting with measurement errors using various noise models. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model. Our work constitutes a step towards finding simple and high-performance decoding strategies for a wide range of quantum low-density parity-check codes.

Highlights

We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes
We show how the sweep decoder can be used to decode phase-flip errors in the 3D toric code on the rhombic dodecahedral lattice with boundaries, and we prove that it has a non-zero error threshold in this case
We focus on the 3D toric code on the rhombic dodecahedral lattice

Summary

Introduction

We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. We numerically benchmark the performance of the decoder in the setting with measurement errors using various noise models We find that this error correction procedure is remarkably robust against measurement errors and is essentially insensitive to the details of the lattice and noise model. Cellular-automaton (CA) decoders for topological c odes[33,34,35,36,37,38,39] are attractive because they are local: at each vertex of the lattice we compute a correction using a simple rule that processes syndrome information in the neighbourhood of the vertex.

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