Localized statistics decoding for quantum low-density parity-check codes
arXiv:2406.18655 · doi:10.1038/s41467-025-63214-7
Abstract
Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to their implementation. In this work, we introduce localized statistics decoding, a reliability-guided inversion decoder that is highly parallelizable and applicable to arbitrary quantum low-density parity-check codes. Our approach employs a parallel matrix factorization strategy, which we call on-the-fly elimination, to identify, validate, and solve local decoding regions on the decoding graph. Through numerical simulations, we show that localized statistics decoding matches the performance of state-of-the-art decoders while reducing the runtime complexity for operation in the sub-threshold regime. Importantly, our decoder is more amenable to implementation on specialized hardware, positioning it as a promising candidate for decoding real-time syndromes from experiments.
accepted version, title change to agree with published version, 23 pages, 12 figures
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- QUITS: A modular Qldpc code circUIT Simulator
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- Towards self-correcting quantum codes for neutral atom arrays
- Unfolded distillation: very low-cost magic state preparation for biased-noise qubits
- Decoding Correlated Errors in Quantum LDPC Codes
- Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory
- Diversity Methods for Improving Convergence and Accuracy of Quantum Error Correction Decoders Through Hardware Emulation
- Benchmarking fault-tolerant quantum computing hardware via QLOPS