We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington [1] which explicitly has a finite speed of communication and computation. For a model of independent X and Z errors and faulty syndrome measurements with identical probability, we report a threshold of 0.133% for this Harrington decoder. We implement a decoder for the 4D toric code which is based on a decoder by Hastings [2]. Incorporating a method for handling faulty syndromes we estimate a threshold of 1.59% for the same noise model as in the 2D case. We compare the performance of this decoder with a decoder based on a 4D version of Toom’s cellular automaton rule as well as the decoding method suggested by Dennis et al.

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Understanding and predicting turbulence in the edge and scrape-off layer (SOL) is critical for the optimization of magnetic confinement fusion devices. While there has been progress along these lines, especially with the help of fluid codes, the development of full- f electromagnetic gyrokinetic codes for the edge and SOL, in general, diverted geometries, remains crucial. In this work, we present simulations of the edge and SOL of the ASDEX Upgrade tokamak with the novel grid-based gyrokinetic (continuum) code GENE-X. The presented simulations are performed at both reduced and realistic electron-to-ion mass ratios on millisecond time scales, studying profile evolution. We compare the resulting plasma profiles to experimental measurements and to previous simulations with the Braginskii fluid code GRILLIX. Furthermore, we measure and validate the SOL power falloff length λq according to the Eich fit function. Based on the results, we discuss the influence of the ion-to-electron mass ratio and collisional effects on gyrokinetic SOL turbulence.