High-threshold topological quantum error correction against biased noise

Abstract

Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can tolerate realistically high error rates will be necessary. In some physical systems, errors may exhibit a characteristic structure that can be carefully exploited to improve the efficacy of error correction. Here, we describe a scheme for topological quantum error correction to protect quantum information from a dephasing-biased error model, where we combine a repetition code with a topological cluster state. We find that the scheme tolerates error rates of up to 1.37%-1.83% per gate, requiring only short-range interactions in a two-dimensional array.

5 pages, 3 figures

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• Erasure qubits: Overcoming the $T_1$ limit in superconducting circuits
• 2-D Compass Codes
• Lindblad Tomography of a Superconducting Quantum Processor
• Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
• General framework for constructing fast and near-optimal machine-learning-based decoder of the topological stabilizer codes
• Improving the lifetime of the NV center ensemble coupled with a superconducting flux qubit by applying magnetic fields
• Identification of different types of high-frequency defects in superconducting qubits
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Generating Fault-Tolerant Cluster States from Crystal Structures
• Fault-tolerant Compass Codes
• Tailored cluster states with high threshold under biased noise
• A cellular automaton decoder for a noise-bias tailored color code
• Benchmarking quantum gates and circuits
• A high threshold code for modular hardware with asymmetric noise
• Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction
• Surface Code with Imperfect Erasure Checks
• Resource optimization for fault-tolerant quantum computing
• Estimating the bias of CX gates via character randomized benchmarking
• Preservation of entanglement in local noisy channels
• Practical quantum error correction with the XZZX code and Kerr-cat qubits
• Mitigating Temporal Fragility in the XY Surface Code
• Bias-preserving computation with the bit-flip code
• Decoding Quantum Error Correction Codes with Local Variation