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001008243 1001_ $$0P:(DE-Juel1)192118$$aOld, Josias$$b0$$eCorresponding author$$ufzj
001008243 245__ $$aGeneralized Belief Propagation Algorithms for Decoding of Surface Codes
001008243 260__ $$aWien$$bVerein zur Förderung des Open Access Publizierens in den Quantenwissenschaften$$c2023
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001008243 520__ $$aBelief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g. notably for the quantum low-density parity check (LDPC) code class of random expander codes. However, it is also well-known that the performance of BP breaks down when facing topological codes such as the surface code, where naive BP fails entirely to reach a below-threshold regime, i.e. the regime where error correction becomes useful. Previous works have shown, that this can be remedied by resorting to post-processing decoders outside the framework of BP. In this work, we present a generalized belief propagation method with an outer re-initialization loop that successfully decodes surface codes, i.e. opposed to naive BP it recovers the sub-threshold regime known from decoders tailored to the surface code and from statistical-mechanical mappings. We report a threshold of 17% under independent bit-and phase-flip data noise (to be compared to the ideal threshold of 20.6%) and a threshold value of 14% under depolarizing data noise (compared to the ideal threshold of 18.9%), which are on par with thresholds achieved by non-BP post-processing methods.
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001008243 7001_ $$0P:(DE-Juel1)187504$$aRispler, Manuel$$b1$$eCorresponding author$$ufzj
001008243 773__ $$0PERI:(DE-600)2931392-2$$a10.22331/q-2023-06-07-1037$$gVol. 7, p. 1037 -$$p1037 -$$tQuantum$$v7$$x2521-327X$$y2023
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