Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors

• URL: http://arxiv.org/abs/2205.02341v1
• Date: Wed, 4 May 2022 22:00:32 GMT
• Title: Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors
• Authors: Nithin Raveendran, Narayanan Rengaswamy, Asit Kumar Pradhan, Bane Vasi\'c
• Abstract summary: 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.
• Score: 10.200716411599831
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are modeled as a binary measurement outcome flipped with some probability. However, the measured syndrome is in fact a discretized value of the continuous voltage or current values obtained in the physical implementation of the syndrome extraction. In this paper, we use this "soft" or analog information without the conventional discretization step to benefit the iterative decoders for decoding quantum low-density parity-check (QLDPC) codes. Syndrome-based iterative belief propagation decoders are modified to utilize the syndrome-soft information to successfully correct both data and syndrome errors simultaneously, without repeated measurements. We demonstrate the advantages of extracting the soft information from the syndrome in our improved decoders, not only in terms of comparison of thresholds and logical error rates for quasi-cyclic lifted-product QLDPC code families, but also for faster convergence of iterative decoders. In particular, the new BP decoder with noisy syndrome performs as good as the standard BP decoder under ideal syndrome.

Related papers

• Degenerate quantum erasure decoding [7.6119527195998025]
  We show how to achieve near-capacity performance with explicit codes and efficient decoders. We furthermore explore the potential of our decoders to handle other error models, such as mixed erasure and depolarizing errors.
  arXiv  Detail & Related papers  (2024-11-20T18:02:05Z)
• A High-Performance List Decoding Algorithm for Surface Codes with Erroneous Syndrome [9.191400697168389]
  We propose a high-performance list decoding algorithm for surface codes with erroneous syndromes. We first use belief propagation (BP) decoding for pre-processing with syndrome soft information, followed by ordered statistics decoding (OSD) for post-processing to list and recover both qubits and syndromes.
  arXiv  Detail & Related papers  (2024-09-11T03:12:18Z)
• Transformer-QEC: Quantum Error Correction Code Decoding with Transferable Transformers [18.116657629047253]
  We introduce a transformer-based Quantum Error Correction (QEC) decoder. It employs self-attention to achieve a global receptive field across all input syndromes. It incorporates a mixed loss training approach, combining both local physical error and global parity label losses.
  arXiv  Detail & Related papers  (2023-11-27T18:52:25Z)
• Testing the Accuracy of Surface Code Decoders [55.616364225463066]
  Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC) This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes.
  arXiv  Detail & Related papers  (2023-11-21T10:22:08Z)
• Improved Noisy Syndrome Decoding of Quantum LDPC Codes with Sliding Window [0.0]
  We study sliding-window decoding, which corrects errors from previous syndrome measurement rounds while leaving the most recent errors for future correction. Remarkably, we find that this improvement may not cost a larger decoding complexity.
  arXiv  Detail & Related papers  (2023-11-06T17:56:49Z)
• Correcting phenomenological quantum noise via belief propagation [7.469588051458094]
  Quantum stabilizer codes often face the challenge of syndrome errors due to error-prone measurements. In this paper, we consider phenomenological decoding problems, where data qubit errors may occur between two syndrome extractions. We propose a method to construct effective redundant stabilizer checks for single-shot error correction.
  arXiv  Detail & Related papers  (2023-10-19T12:23:05Z)
• The END: An Equivariant Neural Decoder for Quantum Error Correction [73.4384623973809]
  We introduce a data efficient neural decoder that exploits the symmetries of the problem. We propose a novel equivariant architecture that achieves state of the art accuracy compared to previous neural decoders.
  arXiv  Detail & Related papers  (2023-04-14T19:46:39Z)
• 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)
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes [61.411482146110984]
  We introduce decoders that are both fast and accurate, and can be used with a wide class of quantum error correction codes. Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC. We find that the decoders led to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code.
  arXiv  Detail & Related papers  (2022-03-09T18:48:54Z)
• 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)

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.