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With the advent of noisy intermediate-scale quantum (NISQ) devices, practical quantum computing has seemingly come into reach.
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It has been claimed that parallelized versions of the MWPM Fowler 2015 or RG decoders Duclos-Cianci and Poulin 2010 can achieve faster than linear decoding time. However, algorithmic scaling of such parallelized algorithms has been discussed in mostly theoretical terms and not demonstrated under realistic conditions yet (e.g. by measuring wall-clock times as done in this manuscript). In particular, we believe that resolving data dependencies will remain a significant bottleneck in any practical implementation
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An impressive optimization of an MWPM implementation has recently been reported using a local variant of the matching decoder Higgott and Breuckmann 2021 in form of the PyMatching package Higgott and Breuckmann , which we use for benchmarking purposes throughout this manuscript
2021
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R. Sweke, M. S. Kesselring, E. P. L. van Nieuwenburg, and J. Eisert, Reinforcement learning decoders for fault-tolerant quantum computation, Machine Learning: Science and Technology 2
2021
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O. Higgott and N. P. Breuckmann, Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead, Phys. Rev. X 11
2021
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