Learning to Decode Concatenated Quantum Codes with Hierarchical Message Passing

• URL: http://arxiv.org/abs/2608.28571v1
• Date: Fri, 28 Aug 2026 17:48:04 GMT
• Title: Learning to Decode Concatenated Quantum Codes with Hierarchical Message Passing
• Abstract summary: We introduce a neural message-passing framework for decoding generald stabilizer codes.<n>For many hypercube codes, a decoder fine-tuned on circuit-level errors in Knill's teleportation-based error correction can achieve lower logical failure rates.
• Score: 6.26319455798863
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a neural message-passing framework for decoding general concatenated stabilizer codes. Soft beliefs propagate bidirectionally across concatenation levels, and lightweight neural networks learn only to aggregate incoming messages. For the concatenated $[[15,7,3]]$ quantum Hamming code, the resulting decoder achieves substantially higher thresholds than the state-of-the-art bidirectional hard-decision decoder under both bit-flip and depolarizing noise. In particular, the depolarizing pseudo-threshold nearly doubles, from $6.5\%$ to $12.3\%$. For many-hypercube codes, a decoder fine-tuned on circuit-level errors in Knill's teleportation-based error correction can achieve lower logical-CNOT failure rates than their dedicated decoder, using a fixed number of message-passing iterations instead of extensive combinatorial search. Our framework provides a generic decoding tool for exploring the design space of concatenated codes, including non-CSS constructions, toward low-overhead fault tolerance.

Related papers

• Efficient foundation decoders for fault-tolerant quantum computing [11.676261938547562]
  We propose a unified framework for efficient foundation decoders.<n>A central feature of NTU is its ability to align decoding tasks across code distances.<n>We instantiate NTU-Transformer as a transformer-based neural decoder.
  arXiv  Detail & Related papers  (2026-06-25T14:58:33Z)
• Beyond Encoder Accumulation: Measuring Encoder Roles in Multi-Encoder VLMs [50.3757247538081]
  We retrain and evaluate all 31 non-empty subsets of five common vision encoders under a unified pipeline.<n>We decompose each encoder's contribution into two axes, Capacity and Necessity.<n>Per-encoder pre-projector effective rank explains the residual score variation.
  arXiv  Detail & Related papers  (2026-06-02T16:46:42Z)
• Bidirectional Decoding for Concatenated Quantum Hamming Codes [6.26319455798863]
  We introduce a hard-decision decoder ford quantum codes with time complexity for scaling.<n>For thed $[15,3]]$ quantum Hamming code under independent bit-flip noise, the bidirectional decoder improves the threshold.<n>Our results can enhance the competitiveness of low-overhead fault-tolerant quantum computation.
  arXiv  Detail & Related papers  (2026-01-14T04:09:37Z)
• Sequential decoding of the XYZ$^2$ hexagonal stabilizer code [0.0]
  We study the XYZ$2$ code, defined on a honeycomb lattice, and use it to decode the syndrome information in two steps.<n>For depolarizing noise we find that the sequential matching decoder gives a threshold of 18.3%, close to optimal.<n>For phase-biased noise on data qubits, at a bias $eta = fracp_zp_x+p_y = 10$, we find that a belief-matching-based decoder reaches thresholds of 24.1%.
  arXiv  Detail & Related papers  (2025-05-06T16:53:51Z)
• Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction [44.698141103370546]
  GraphQEC is a code-agnostic decoder leveraging machine-learning on the graph structure of stabilizer codes with linear time complexity.<n>Our approach represents the first universal solution for real-time quantum error correction across arbitrary stabilizer codes.
  arXiv  Detail & Related papers  (2025-02-27T10:56:53Z)
• Generalizing the matching decoder for the Chamon code [1.8416014644193066]
  We implement variations of a matching decoder for a three-dimensional, non-CSS, low-density parity check code known as the Chamon code.<n>We find that a generalized matching decoder that is augmented by a belief-propagation step prior to matching gives a threshold of 10.5% for depolarizing noise.
  arXiv  Detail & Related papers  (2024-11-05T19:00:12Z)
• Learning Linear Block Error Correction Codes [62.25533750469467]
  We propose for the first time a unified encoder-decoder training of binary linear block codes. We also propose a novel Transformer model in which the self-attention masking is performed in a differentiable fashion for the efficient backpropagation of the code gradient.
  arXiv  Detail & Related papers  (2024-05-07T06:47:12Z)
• 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)
• Quantum computation on a 19-qubit wide 2d nearest neighbour qubit array [59.24209911146749]
  This paper explores the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds. We engineer an error bias at the lowest level of encoding using the surface code. We then address this bias at a higher level of encoding using a lattice-surgery surface code bus.
  arXiv  Detail & Related papers  (2022-12-03T06:16:07Z)
• 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)
• Trellis Decoding For Qudit Stabilizer Codes And Its Application To Qubit Topological Codes [3.9962751777898955]
  We show that trellis decoders have strong structure, extend the results using classical coding theory as a guide, and demonstrate a canonical form from which the structural properties of the decoding graph may be computed. The modified decoder works for any stabilizer code $S$ and separates into two parts: a one-time, offline which builds a compact, graphical representation of the normalizer of the code, $Sperp$, and a quick, parallel, online computation using the Viterbi algorithm.
  arXiv  Detail & Related papers  (2021-06-15T16:01:42Z)
• Pruning Neural Belief Propagation Decoders [77.237958592189]
  We introduce a method to tailor an overcomplete parity-check matrix to (neural) BP decoding using machine learning. We achieve performance within 0.27 dB and 1.5 dB of the ML performance while reducing the complexity of the decoder.
  arXiv  Detail & Related papers  (2020-01-21T12:05:46Z)

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.