Linear-time general decoding algorithm for the surface code

Abstract

A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including coherences and correlations. We demonstrate that the decoder significantly outperforms the conventional matching algorithm on a variety of noise models, including non-Pauli noise and spatially correlated noise. The algorithm is based on an approximate calculation of the logical channel using a tensor-network description of the noisy state.

5 pages, 2 figures; v2 published version

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• Quantum Error Correction with the Semion Code
• 2-D Compass Codes
• Density Matrix Renormalization Group with Tensor Processing Units
• A local pre-decoder to reduce the bandwidth and latency of quantum error correction
• Tensor-network codes
• Neural ensemble decoding for topological quantum error-correcting codes
• Pauli channels can be estimated from syndrome measurements in quantum error correction
• Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
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• Achieving fault tolerance on capped color codes with few ancillas
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• Local tensor-network codes
• Low-depth random Clifford circuits for quantum coding against Pauli noise using a tensor-network decoder
• Practical quantum error correction with the XZZX code and Kerr-cat qubits
• Bayesian inference of general noise-model parameters from the syndrome statistics of surface codes