Optimal error correction in topological subsystem codes

Abstract

A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing for error syndrome recovery with only 2-local measurements in a two-dimensional array of qubits. We study the error threshold for topological subsystem color codes under very general external noise conditions. By transforming the problem into a classical disordered spin model, we estimate using Monte Carlo simulations that topological subsystem codes have an optimal error tolerance of 5.5(2)%. This means there is ample space for improvement in existing error-correcting algorithms that typically find a threshold of approximately 2%.

4 pages, 4 figures, 4 authors

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Cited by in corpus (16)

• Quantum Error Correction for Beginners
• Hamiltonian Learning for Quantum Error Correction
• Scalable in-situ qubit calibration during repetitive error detection
• Classical simulation of non-Gaussian fermionic circuits
• Pipelined correlated minimum weight perfect matching of the surface code
• Error tolerance of topological codes with independent bit-flip and measurement errors
• The role of entropy in topological quantum error correction
• Dual correspondence between classical spin models and quantum CSS states
• Topological Subsystem Codes From Graphs and Hypergraphs
• Accurate simulations of planar topological codes cannot use cyclic boundaries
• Optimal quantum subsystem codes in 2-dimensions
• Learning to find order in disorder
• Stability of topologically-protected quantum computing proposals as seen through spin glasses
• Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat's Lemma
• 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