Localized statistics decoding for quantum low-density parity-check codes

TL;DR

This paper introduces a new localized statistics decoding method for quantum low-density parity-check codes, offering a highly parallelizable, efficient, and hardware-friendly decoder that matches state-of-the-art performance.

Contribution

The paper presents a novel, highly parallelizable decoding algorithm for quantum LDPC codes using localized statistics and on-the-fly elimination, suitable for real-time quantum error correction.

Findings

Matches performance of state-of-the-art decoders

Reduces runtime complexity in the sub-threshold regime

More suitable for implementation on specialized hardware

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.