Error tolerance of topological codes with independent bit-flip and measurement errors

Abstract

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).

6 pages, 3 figures

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• Hamiltonian Learning for Quantum Error Correction
• A decoder for the triangular color code by matching on a Möbius strip
• Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
• The role of entropy in topological quantum error correction
• Dual correspondence between classical spin models and quantum CSS states
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Fundamental thresholds of realistic quantum error correction circuits from classical spin models
• Ising model formulation for highly accurate topological color codes decoding
• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder
• Noisy Toric code and random bond Ising model: The error threshold in a dual picture
• The geometric phase transition of the three-dimensional ${\mathbb{Z}}_2$ lattice gauge model