Correcting non-independent and non-identically distributed errors with surface codes

Abstract

A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern multi-qubit devices are typically neither independent nor identical across qubits. In this work, we develop and investigate the properties of topological surface codes adapted to a known noise structure by Clifford conjugations. We show that the surface code locally tailored to non-uniform single-qubit noise in conjunction with a scalable matching decoder yields an increase in error thresholds and exponential suppression of sub-threshold failure rates when compared to the standard surface code. Furthermore, we study the behaviour of the tailored surface code under local two-qubit noise and show the role that code degeneracy plays in correcting such noise. The proposed methods do not require additional overhead in terms of the number of qubits or gates and use a standard matching decoder, hence come at no extra cost compared to the standard surface-code error correction.

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• Analog information decoding of bosonic quantum LDPC codes
• Designing fault-tolerant circuits using detector error models
• Modeling error correction with Lindblad dynamics and approximate channels
• Quantum computer error structure probed by quantum error correction syndrome measurements
• The domain wall color code
• Exact results on finite size corrections for surface codes tailored to biased noise
• On the Efficacy of Surface Codes in Compensating for Radiation Events in Superconducting Devices
• Multi-Qubit Parity Gates for Rydberg Atoms in Various Configurations
• Rare Events and Griffiths Phases in Topological Quantum Error Correction
• Mitigating cosmic ray-like correlated events with a modular quantum processor
• Entanglement boosting: Low-volume logical Bell pair preparation for distributed fault-tolerant quantum computation
• Hardness results for decoding the surface code with Pauli noise
• Symmetry in Multi-Qubit Correlated Noise Errors Enhances Surface Code Thresholds
• Spin-augmented observables for efficient photonic quantum error correction