Localized statistics decoding: A parallel decoding algorithm for quantum low-density parity-check codes

• URL: http://arxiv.org/abs/2406.18655v1
• Date: Wed, 26 Jun 2024 18:00:09 GMT
• Title: Localized statistics decoding: A parallel decoding algorithm for quantum low-density parity-check codes
• Authors: Timo Hillmann, Lucas Berent, Armanda O. Quintavalle, Jens Eisert, Robert Wille, Joschka Roffe,
• Abstract summary: We introduce localized statistics decoding for arbitrary quantum low-density parity-check codes. Our decoder is more amenable to implementation on specialized hardware, positioning it as a promising candidate for decoding real-time syndromes from experiments.
• Score: 3.001631679133604
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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