Decoding three-dimensional color codes with boundaries

RWTH Publications (RWTH Aachen)

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 et al., Quantum 9, 1609 (2025)], 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, Phys. Rev. A 89, 012317 (2014); S. Turner et al., arXiv:2003.11602].We furthermore present QCODEPLOT3D, a PYTHON 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.

Authors 3

1. Friederike Butt Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

2. Lars Esser Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

3. Markus Müller Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen