Generalized Belief Propagation Algorithms for Decoding of Surface Codes

Quantum, vol. 7, pp. 1037

Abstract

Belief 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.

Authors 2

1. Josias Old Aachen Institute for Quantum Information

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University, Aachen, Germany

   Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich, Jülich, Germany

2. Manuel Rispler Aachen Institute for Quantum Information

   RWTH Aachen University · Forschungszentrum Jülich · QuTech · Delft University of Technology

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University, Aachen, Germany

   Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich, Jülich, Germany

   QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands