Fast Fault-Tolerant Decoders for Hypergraph Product and Lifted-Product Codes

• URL: http://arxiv.org/abs/2608.31040v1
• Date: Mon, 31 Aug 2026 16:18:29 GMT
• Title: Fast Fault-Tolerant Decoders for Hypergraph Product and Lifted-Product Codes
• Abstract summary: We design low-complexity, fault-tolerant decoders for quantum low-density parity-check (QLDPC) codes.<n>We target two major bottlenecks of decoding under the emphcircuit-level noise model.
• Score: 1.9365949510386082
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We design low-complexity, fault-tolerant decoders for quantum low-density parity-check (QLDPC) codes with the goal of reducing decoding latency. We target two major bottlenecks of decoding under the \emph{circuit-level} noise model: (i) post-processing via order-statistics decoding (OSD), and (ii) the large number of auxiliary variable nodes commonly introduced to represent CNOT-induced correlations during syndrome extraction. Our key observation is that propagating CNOT faults (\emph{hook errors}) create \emph{stabilizer-induced} trapping sets (TSs) that are intrinsic to hypergraph-product (HGP) and lifted-product (LP) constructions. Therefore, instead of modeling each such fault with an explicit correlation node and relying on OSD to clean up the resulting failures, we design message-passing decoders that resolve the corresponding \emph{stabilizer-induced} TSs directly. We obtain these decoders by deriving QLDPC decoders from decoders for the parent classical LDPC codes and using them collectively to correct broad families of \emph{stabilizer-induced} TSs. For CNOT faults that manifest primarily as syndrome errors, we show that their effect is equivalent to a data error together with syndrome-bit measurement errors. Consequently, given repeated measurements and a decoding graph that already includes nodes representing syndrome-bit errors, no distinct variable node is needed for each CNOT fault. Using a \emph{phenomenological} Tanner graph with nodes representing only data errors and syndrome-bit errors, simulations on the LP codes show a reduction in, or comparable, logical error rates relative to BP+OSD, at substantially lower decoding complexity.

Related papers

• The Gain-Engineered Transmon [68.89136228609398]
  We introduce and experimentally realize a noise-biased qubit in a standard transmon-readout resonator circuit.<n>Our results open a path towards using this system as a simple building-block for hardware-efficient quantum error detection and correction schemes.
  arXiv  Detail & Related papers  (2026-08-26T17:00:42Z)
• From Early Encoding to Late Suppression: Interpreting LLMs on Character Counting Tasks [49.57538588967748]
  Large language models (LLMs) exhibit failures on elementary symbolic tasks such as character counting in a word, despite excelling on complex benchmarks.<n>We uncover a consistent phenomenon across modern architectures, including LLaMA, Qwen, and Gemma.<n>We show that symbolic reasoning failures in LLMs are not due to missing representations or insufficient scale, but arise from structured interference within the model's computation graph.
  arXiv  Detail & Related papers  (2026-04-01T11:40:12Z)
• Generalizing GNNs with Tokenized Mixture of Experts [75.8310720413187]
  We show that improving stability requires reducing reliance on shift-sensitive features, leaving an irreducible worst-case generalization floor.<n>We propose STEM-GNN, a pretrain-then-finetune framework with a mixture-of-experts encoder for diverse computation paths.<n>Across nine node, link, and graph benchmarks, STEM-GNN achieves a stronger three-way balance, improving robustness to degree/homophily shifts and to feature/edge corruptions while remaining competitive on clean graphs.
  arXiv  Detail & Related papers  (2026-02-09T22:48:30Z)
• Turbo-Annihilation of Hook Errors in Stabilizer Measurement Circuits [2.6999000177990924]
  We propose a scalable decoding framework for correcting correlated hook errors in stabilizer measurement circuits.<n>Traditional circuit-level decoding attempts to estimate the precise location of faults by constructing an extended Tanner graph.<n>Our approach instead focuses on estimating the effective data errors caused by hook faults, modeling them as memory channels.
  arXiv  Detail & Related papers  (2025-04-29T22:09:11Z)
• Adaptive Syndrome Extraction [1.9686770963118383]
  We introduce adaptive syndrome extraction as a scheme to improve code performance and reduce the quantum error correction cycle time.<n>Compared to non-concatenated codes and non-adaptive syndrome extraction, we find that the adaptive scheme achieves over an order of magnitude lower logical error rates.
  arXiv  Detail & Related papers  (2025-02-20T18:48:32Z)
• An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise [0.562479170374811]
  Fault-tolerant quantum computers must be designed in conjunction with classical co-processors.<n>We introduce the belief propagation plus ordered Tanner forest (BP+OTF) algorithm as an almost-linear time decoder for quantum low-density parity-check codes.
  arXiv  Detail & Related papers  (2024-09-02T19:50:57Z)
• Fault-tolerant quantum architectures based on erasure qubits [49.227671756557946]
  We exploit the idea of erasure qubits, relying on an efficient conversion of the dominant noise into erasures at known locations. We propose and optimize QEC schemes based on erasure qubits and the recently-introduced Floquet codes. Our results demonstrate that, despite being slightly more complex, QEC schemes based on erasure qubits can significantly outperform standard approaches.
  arXiv  Detail & Related papers  (2023-12-21T17:40:18Z)
• Generalized quantum data-syndrome codes and belief propagation decoding for phenomenological noise [6.322831694506286]
  We introduce quantum data-syndrome codes along with a generalized check matrix that integrates both quaternary and binary alphabets to represent diverse error sources.<n>We observe that at high error rates, fewer rounds of syndrome extraction tend to perform better, while more rounds improve performance at lower error rates.
  arXiv  Detail & Related papers  (2023-10-19T12:23:05Z)
• 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)
• Witnessing entanglement in trapped-ion quantum error correction under realistic noise [41.94295877935867]
  Quantum Error Correction (QEC) exploits redundancy by encoding logical information into multiple physical qubits. We present a detailed microscopic error model to estimate the average gate infidelity of two-qubit light-shift gates used in trapped-ion platforms. We then apply this realistic error model to quantify the multipartite entanglement generated by circuits that act as QEC building blocks.
  arXiv  Detail & Related papers  (2022-12-14T20:00:36Z)
• Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors [10.200716411599831]
  Quantum errors are primarily detected and corrected using the measurement of syndrome information. In this paper, we use this "soft" or analog information without the conventional discretization step. We demonstrate the advantages of extracting the soft information from the syndrome in our improved decoders.
  arXiv  Detail & Related papers  (2022-05-04T22:00:32Z)
• Reducing Redundancy in the Bottleneck Representation of the Autoencoders [98.78384185493624]
  Autoencoders are a type of unsupervised neural networks, which can be used to solve various tasks. We propose a scheme to explicitly penalize feature redundancies in the bottleneck representation. We tested our approach across different tasks: dimensionality reduction using three different dataset, image compression using the MNIST dataset, and image denoising using fashion MNIST.
  arXiv  Detail & Related papers  (2022-02-09T18:48:02Z)

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.