Decoding three-dimensional color codes with boundaries

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Abstract
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are promising candidates for fault-tolerant quantum computation due to their transversal non-Clifford gates, but efficient decoding remains challenging. In this work, we extend previous decoders for two-dimensional color codes [S.-H. Lee , ], which are based on the restriction of the decoding problem to a subset of the qubit lattice, to three dimensions. Including boundaries of 3D color codes, we demonstrate that the 3D restriction decoder achieves optimal scaling of the logical error rate and a threshold value of 1.55(6)% for code-capacity bit- and phase-flip noise, which is almost a factor of 2 higher than previously reported for this family of codes [N. Delfosse, ; S. Turner , ]. We furthermore present , a package for visualizing two-dimensional and 3D color codes, error configurations, and decoding paths, which supports the development and analysis of such decoders. These advancements contribute to making 3D color codes a more practical option for exploring fault-tolerant quantum computation.
Funding Information
  • European Commission (101114305)
  • Bundesministerium für Forschung, Technologie und Raumfahrt (13N17317)
  • Bundesministerium für Forschung, Technologie und Raumfahrt (13N16070)
  • Intelligence Advanced Research Projects Activity (W911NF-23-2-0216)
  • European Research Council (804247)
  • Deutsche Forschungsgemeinschaft (390534769)
  • Naval Health Research Center
  • RWTH Aachen University (p0020074)

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