Decoding color codes by projection onto surface codes

Abstract

We propose a new strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes. Applying this idea to a family of hexagonal color codes, with the perfect matching decoding algorithm for the three corresponding surface codes, we find a phase error threshold of approximately 8.7%. Finally, our approach enables us to establish a general lower bound on the error threshold of a family of color codes depending on the threshold of the three corresponding surface codes. These results are based on a chain complex interpretation of surface codes and color codes.

24 pages

References in corpus (5)

• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• Topological fault-tolerance in cluster state quantum computation
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Homological Error Correction: Classical and Quantum Codes

Cited by in corpus (61)

• Roads towards fault-tolerant universal quantum computation
• Almost-linear time decoding algorithm for topological codes
• Unfolding the color code
• Fault-tolerant thresholds for quantum error correction with the surface code
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Fault-tolerant error correction with the gauge color code
• Triangular color codes on trivalent graphs with flag qubits
• The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes
• Advantages of versatile neural-network decoding for topological codes
• Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
• A fault-tolerant non-Clifford gate for the surface code in two dimensions
• Neural network decoder for topological color codes with circuit level noise
• Cellular-automaton decoders with provable thresholds for topological codes
• Parallelized quantum error correction with fracton topological codes
• Analysing correlated noise on the surface code using adaptive decoding algorithms
• Three-dimensional color code thresholds via statistical-mechanical mapping
• Multi-path Summation for Decoding 2D Topological Codes
• Qudit Colour Codes and Gauge Colour Codes in All Spatial Dimensions
• Exploiting Degeneracy in Belief Propagation Decoding of Quantum Codes
• Quantum computing by color-code lattice surgery
• A local pre-decoder to reduce the bandwidth and latency of quantum error correction
• Gauge color codes in two dimensions
• Benchmarking near-term devices with quantum error correction
• Morphing quantum codes
• A decoder for the triangular color code by matching on a Möbius strip
• General framework for constructing fast and near-optimal machine-learning-based decoder of the topological stabilizer codes
• Efficient color code decoders in $d\ge 2$ dimensions from toric code decoders
• Quantum computation from dynamic automorphism codes
• Noise Thresholds for the [[4, 2, 2]]-concatenated Toric Code
• Quantum Computation with Topological Codes: from qubit to topological fault-tolerance
• A four-dimensional toric code with non-Clifford transversal gates
• A decoding algorithm for CSS codes using the X/Z correlations
• Achieving fault tolerance on capped color codes with few ancillas
• Quantum error correction with the color-Gottesman-Kitaev-Preskill code
• Projecting 3D color codes onto 3D toric codes
• Color code decoder with improved scaling for correcting circuit-level noise
• Data-driven decoding of quantum error correcting codes using graph neural networks
• Quantum Pin Codes
• Decoding quantum color codes with MaxSAT
• CSS code surgery as a universal construction
• Universal resource-efficient topological measurement-based quantum computation via color-code-based cluster states
• Comparison of 2D topological codes and their decoding performances
• Improved quantum error correction using soft information
• Comparison of memory thresholds for planar qudit geometries
• Low-overhead magic state distillation with color codes
• Concatenated Steane code with single-flag syndrome checks
• The domain wall color code
• Rescaling decoder for 2D topological quantum color codes on 4.8.8 lattices
• Optimization tools for distance-preserving flag fault-tolerant error correction
• On the Local Equivalence of 2D Color Codes and Surface Codes with Applications
• Magic Mirror on the Wall, How to Benchmark Quantum Error Correction Codes, Overall ?
• Enhancing Quantum Memory Lifetime with Measurement-Free Local Error Correction and Reinforcement Learning
• Distributed Realization of Color Codes for Quantum Error Correction
• Single-shot quantum error correction with the three-dimensional subsystem toric code
• Generalizing the matching decoder for the Chamon code
• Layer-by-layer disentangling two-dimensional topological quantum codes
• Decoding Algorithms for Hypergraph Subsystem Codes and Generalized Subsystem Surface Codes
• Pseudocodeword-based Decoding of Quantum Color Codes
• On the interpretability of neural network decoders
• Planar fault-tolerant circuits for non-Clifford gates on the 2D color code