Cyclic Hypergraph Product Code

• URL: http://arxiv.org/abs/2511.09683v1
• Date: Fri, 14 Nov 2025 01:04:10 GMT
• Title: Cyclic Hypergraph Product Code
• Authors: Arda Aydin, Nicolas Delfosse, Edwin Tham,
• Abstract summary: We study the hypergraph product of two cyclic codes, which we call CxC codes and CxR codes.<n>We discover C2 codes and CxR codes that significantly outperform previously optimized HGP codes.<n>Some C2 codes achieve simultaneously a lower logical error rate and a smaller qubit overhead than state-of-the-art LDPC codes.
• Score: 1.338174941551702
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hypergraph product (HGP) codes are one of the most popular family of quantum low-density parity-check (LDPC) codes. Circuit-level simulations show that they can achieve the same logical error rate as surface codes with a reduced qubit overhead. They have been extensively optimized by importing classical techniques such as the progressive edge growth, or through random search, simulated annealing or reinforcement learning techniques. In this work, instead of machine learning (ML) algorithms that improve the code performance through local transformations, we impose additional global symmetries, that are hard to discover through ML, and we perform an exhaustive search. Precisely, we focus on the hypergraph product of two cyclic codes, which we call CxC codes and we study C2 codes which are the product a cyclic code with itself and CxR codes which are the product of a cyclic codes with a repetition code. We discover C2 codes and CxR codes that significantly outperform previously optimized HGP codes, achieving better parameters and a logical error rate per logical qubit that is up to three orders of magnitude better. Moreover, some C2 codes achieve simultaneously a lower logical error rate and a smaller qubit overhead than state-of-the-art LDPC codes such as the bivariate bicycle codes, at the price of a larger block length. Finally, leveraging the cyclic symmetry imposed on the codes, we design an efficient planar layout for the QCCD architecture, allowing for a trapped ion implementation of the syndrome extraction circuit in constant depth.

Related papers

• A matching decoder for bivariate bicycle codes [0.8739101659113153]
  We propose a method we call the 'cylinder trick' to rapidly find a correction using matching on code symmetries.<n>We benchmark our decoder on the gross code family, cyclic hypergraph-product codes, generalized toric codes, and recently proposed directional codes.<n>For a subset of these codes, we find that our decoder can be significantly improved by augmenting matching with strategies including belief propagation and 'over-matching'
  arXiv  Detail & Related papers  (2026-02-26T09:00:20Z)
• Constant-Overhead Addressable Gates via Single-Shot Code Switching [1.6822770693792826]
  It is a major challenge to perform addressable and parallel logical operations on constantrate quantum LDPC (qLDPC) codes.<n>We introduce fault-tolerant protocols for performing various addressable gadgets as well as parallel logical operations with constant space-time overhead.
  arXiv  Detail & Related papers  (2025-10-08T08:37:50Z)
• Abelian multi-cycle codes for single-shot error correction [0.013727765507558195]
  We construct a family of quantum low-density parity-check codes locally equivalent to higher-dimensional quantum hypergraph-product (QHP) codes.<n>The proposed codes have highly redundant sets of low-weight stabilizer generators, which improves decoding accuracy in a fault-tolerant regime.<n>We derive simple expressions for the dimension of the proposed codes in two important special cases, give bounds on the distances, and explicitly construct some relatively short codes.
  arXiv  Detail & Related papers  (2025-06-20T11:05:32Z)
• Fast correlated decoding of transversal logical algorithms [67.01652927671279]
  Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead.<n>Recent advances have shown that by jointly decoding logical qubits in algorithms composed of logical gates, the number of syndrome extraction rounds can be reduced.<n>Here, we reform the problem of decoding circuits by directly decoding relevant logical operator products as they propagate through the circuit.
  arXiv  Detail & Related papers  (2025-05-19T18:00:00Z)
• Decoding Quasi-Cyclic Quantum LDPC Codes [23.22566380210149]
  Quantum low-density parity-check (qLDPC) codes are an important component in the quest for fault tolerance. Recent progress on qLDPC codes has led to constructions which are quantumally good, and which admit linear-time decoders to correct errors affecting a constant fraction of codeword qubits. In practice, the surface/toric codes, which are the product of two repetition codes, are still often the qLDPC codes of choice.
  arXiv  Detail & Related papers  (2024-11-07T06:25:27Z)
• Factor Graph Optimization of Error-Correcting Codes for Belief Propagation Decoding [62.25533750469467]
  Low-Density Parity-Check (LDPC) codes possess several advantages over other families of codes. The proposed approach is shown to outperform the decoding performance of existing popular codes by orders of magnitude.
  arXiv  Detail & Related papers  (2024-06-09T12:08:56Z)
• 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)
• Spatially-Coupled QLDPC Codes [3.1000291317724997]
  We describe toric codes as quantum counterparts of classical spatially-coupled (2D-SC) codes.<n>We introduce spatially-coupled quantum LDPC (SC-QLDPC) codes as a class of convolutional LDPC codes.<n>This paper focuses on QLDPC codes with rate less than 1/10, but we construct 2D-SC HGP codes with small memories, higher rates (about 1/3), and superior thresholds.
  arXiv  Detail & Related papers  (2023-04-29T00:57:57Z)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [47.52324012811181]
  homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code.<n>We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
  arXiv  Detail & Related papers  (2023-03-24T00:29:15Z)
• 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)
• Tailored XZZX codes for biased noise [60.12487959001671]
  We study a family of codes having XZZX-type stabilizer generators. We show that these XZZX codes are highly qubit efficient if tailored to biased noise.
  arXiv  Detail & Related papers  (2022-03-30T17:26:31Z)
• KO codes: Inventing Nonlinear Encoding and Decoding for Reliable Wireless Communication via Deep-learning [76.5589486928387]
  Landmark codes underpin reliable physical layer communication, e.g., Reed-Muller, BCH, Convolution, Turbo, LDPC and Polar codes. In this paper, we construct KO codes, a computationaly efficient family of deep-learning driven (encoder, decoder) pairs. KO codes beat state-of-the-art Reed-Muller and Polar codes, under the low-complexity successive cancellation decoding.
  arXiv  Detail & Related papers  (2021-08-29T21:08:30Z)

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.