Efficient Mitigation of Error Floors in Quantum Error Correction using Non-Binary Low-Density Parity-Check Codes

• URL: http://arxiv.org/abs/2501.13923v1
• Date: Thu, 23 Jan 2025 18:59:08 GMT
• Title: Efficient Mitigation of Error Floors in Quantum Error Correction using Non-Binary Low-Density Parity-Check Codes
• Authors: Kenta Kasai,
• Abstract summary: We identify and classify cycle structures in the parity-check matrix where estimated noise becomes trapped.<n>For Type-I cycles, we propose a method to make the difference between estimated and true noise degenerate.<n>Type-II cycles are shown to be uncorrectable, while for Type-III cycles, we utilize the fact that cycles in non-binary LDPC codes do not necessarily correspond to codewords.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated noise becomes trapped, and develop tailored decoding methods for each cycle type. For Type-I cycles, we propose a method to make the difference between estimated and true noise degenerate. Type-II cycles are shown to be uncorrectable, while for Type-III cycles, we utilize the fact that cycles in non-binary LDPC codes do not necessarily correspond to codewords, allowing us to estimate the true noise. Our method significantly improves decoding performance and reduces error floors.

Related papers

• Quantum Error Correction with Girth-16 Non-Binary LDPC Codes via Affine Permutation Construction [0.0]
  We propose a method for constructing quantum error-correcting codes based on non-binary low-density parity-check codes with Tanner graph girth 16. Numerical experiments show that the proposed codes significantly reduce the number of low-weight codewords.
  arXiv  Detail & Related papers  (2025-04-24T17:59:58Z)
• Approximate Quantum Error Correction with 1D Log-Depth Circuits [0.824969449883056]
  We construct quantum error-correcting codes based on one-dimensional, logarithmic-depth random Clifford encoding circuits with a two-layer circuit structure. We show that the error correction inaccuracy decays exponentially with circuit depth, resulting in negligible errors for these logarithmic-depth circuits.
  arXiv  Detail & Related papers  (2025-03-22T12:54:04Z)
• Threshold Selection for Iterative Decoding of $(v,w)$-regular Binary Codes [84.0257274213152]
  Iterative bit flipping decoders are an efficient choice for sparse $(v,w)$-regular codes.<n>We propose concrete criteria for threshold determination, backed by a closed form model.
  arXiv  Detail & Related papers  (2025-01-23T17:38:22Z)
• Explicit Construction of Classical and Quantum Quasi-Cyclic Low-Density Parity-Check Codes with Column Weight 2 and Girth 12 [0.0]
  This study proposes an explicit construction method for classical and quantum quasi-cyclic low-density parity-check codes with a girth of 12.<n>By utilizing algebraic techniques, short cycles are eliminated, which improves error correction performance.<n>The results of this study enable the design of high-performance quantum error correction codes without the need for random search.
  arXiv  Detail & Related papers  (2025-01-23T07:52:07Z)
• Estimating the Decoding Failure Rate of Binary Regular Codes Using Iterative Decoding [84.0257274213152]
  We propose a new technique to provide accurate estimates of the DFR of a two-iterations (parallel) bit flipping decoder.<n>We validate our results, providing comparisons of the modeled and simulated weight of the syndrome, incorrectly-guessed error bit distribution at the end of the first iteration, and two-itcrypteration Decoding Failure Rates (DFR)
  arXiv  Detail & Related papers  (2024-01-30T11:40:24Z)
• 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)
• Estimating Coherent Contributions to the Error Profile Using Cycle Error Reconstruction [0.0]
  We present a scalable and cycle-centric methodology for obtaining a detailed estimate of the coherent contribution to the error profile of a hard computing cycle. We perform proof-of-concept experiments on three IBM chips, namely ibmq_guadalupe, ibmq_manila, and ibmq_montreal.
  arXiv  Detail & Related papers  (2023-03-17T13:04:19Z)
• 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)
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [58.720142291102135]
  We analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.
  arXiv  Detail & Related papers  (2021-08-02T16:12:13Z)
• Autoregressive Belief Propagation for Decoding Block Codes [113.38181979662288]
  We revisit recent methods that employ graph neural networks for decoding error correcting codes. Our method violates the symmetry conditions that enable the other methods to train exclusively with the zero-word. Despite not having the luxury of training on a single word, and the inability to train on more than a small fraction of the relevant sample space, we demonstrate effective training.
  arXiv  Detail & Related papers  (2021-01-23T17:14:55Z)
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits [58.720142291102135]
  We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) We prove that the detection of entanglement in a linear number of bipartitions by a number of measurements scales linearly, suffices to certify GME. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version.
  arXiv  Detail & Related papers  (2020-10-06T18:00:07Z)

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.