SymBreak: Mitigating Quantum Degeneracy Issues in QLDPC Code Decoders by Breaking Symmetry

• URL: http://arxiv.org/abs/2412.02885v1
• Date: Tue, 03 Dec 2024 22:45:43 GMT
• Title: SymBreak: Mitigating Quantum Degeneracy Issues in QLDPC Code Decoders by Breaking Symmetry
• Authors: Keyi Yin, Xiang Fang, Jixuan Ruan, Hezi Zhang, Dean Tullsen, Andrew Sornborger, Chenxu Liu, Ang Li, Travis Humble, Yufei Ding,
• Abstract summary: Quantum low-density parity check (qLDPC) codes have emerged as a promising alternative, requiring fewer qubits. SymBreak is a novel decoder for qLDPC codes that adaptively modifies the decoding graph to improve the performance of state-of-the-art belief propagation decoders. Our results demonstrate that SymBreak outperforms BP and BP+OSD-a more complex variant of BP-with a $16.17times$ reduction in logical error rate compared to BP and $3.23times$ compared to BP+OSD across various qLDPC code families.
• Score: 13.97553415798807
• License:
• Abstract: Quantum error correction (QEC) is critical for scalable and reliable quantum computing, but existing solutions, such as surface codes, incur significant qubit overhead. Quantum low-density parity check (qLDPC) codes have recently emerged as a promising alternative, requiring fewer qubits. However, the lack of efficient decoders remains a major barrier to their practical implementation. In this work, we introduce SymBreak, a novel decoder for qLDPC codes that adaptively modifies the decoding graph to improve the performance of state-of-the-art belief propagation (BP) decoders. Our key contribution is identifying quantum degeneracy as a root cause of the convergence issues often encountered in BP decoding of quantum LDPC codes. We propose a solution that mitigates this issue at the decoding graph level, achieving both fast and accurate decoding. Our results demonstrate that SymBreak outperforms BP and BP+OSD-a more complex variant of BP-with a $16.17\times$ reduction in logical error rate compared to BP and $3.23\times$ compared to BP+OSD across various qLDPC code families. With only an $18.97$% time overhead compared to BP, SymBreak provides significantly faster decoding times than BP+OSD, representing a major advancement in efficient and accurate decoding for qLDPC-based QEC architectures.

Related papers

• Ambiguity Clustering: an accurate and efficient decoder for qLDPC codes [0.0]
  We introduce the Ambiguity Clustering decoder (AC) which divides measurement data into clusters that can be decoded independently. With 0.3% circuit-level depolarising noise, AC is up to 27x faster than BP-OSD with matched accuracy. Our implementation decodes the 144-qubit Gross code in 135us per round of syndrome extraction on an M2 CPU.
  arXiv  Detail & Related papers  (2024-06-20T17:39:31Z)
• Belief Propagation Decoding of Quantum LDPC Codes with Guided Decimation [55.8930142490617]
  We propose a decoder for QLDPC codes based on BP guided decimation (BPGD) BPGD significantly reduces the BP failure rate due to non-convergence.
  arXiv  Detail & Related papers  (2023-12-18T05:58:07Z)
• Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes with Overcomplete Check Matrices [45.997444794696676]
  Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. We first propose to decode QLDPC codes with a belief propagation (BP) decoder operating on overcomplete check matrices. We extend the neural BP (NBP) decoder, which was originally studied for suboptimal binary BP decoding of QLPDC codes, to quaternary BP decoders.
  arXiv  Detail & Related papers  (2023-08-16T08:24:06Z)
• Modular decoding: parallelizable real-time decoding for quantum computers [55.41644538483948]
  Real-time quantum computation will require decoding algorithms capable of extracting logical outcomes from a stream of data generated by noisy quantum hardware. We propose modular decoding, an approach capable of addressing this challenge with minimal additional communication and without sacrificing decoding accuracy. We introduce the edge-vertex decomposition, a concrete instance of modular decoding for lattice-surgery style fault-tolerant blocks.
  arXiv  Detail & Related papers  (2023-03-08T19:26:10Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices [60.02503434201552]
  We propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix. This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency.
  arXiv  Detail & Related papers  (2022-12-20T13:41:27Z)
• Graph Neural Networks for Channel Decoding [71.15576353630667]
  We showcase competitive decoding performance for various coding schemes, such as low-density parity-check (LDPC) and BCH codes. The idea is to let a neural network (NN) learn a generalized message passing algorithm over a given graph. We benchmark our proposed decoder against state-of-the-art in conventional channel decoding as well as against recent deep learning-based results.
  arXiv  Detail & Related papers  (2022-07-29T15:29:18Z)
• Refined Belief-Propagation Decoding of Quantum Codes with Scalar Messages [4.340338299803562]
  Codes based on sparse matrices have good performance and can be efficiently decoded by belief-propagation (BP) BP decoding of stabilizer codes suffers a performance loss from the short cycles in the underlying Tanner graph. We show that running BP with message normalization according to a serial schedule may significantly improve the decoding performance and error-floor in computer simulation.
  arXiv  Detail & Related papers  (2021-02-14T10:29:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.