Efficient soft-output decoders for the surface code

• URL: http://arxiv.org/abs/2405.07433v2
• Date: Sat, 1 Jun 2024 23:23:37 GMT
• Title: Efficient soft-output decoders for the surface code
• Authors: Nadine Meister, Christopher A. Pattison, John Preskill,
• Abstract summary: We construct efficient soft-output decoders for the surface code derived from the Minimum-Weight Perfect Matching and Union-Find decoders. We show that soft-output decoding can improve the performance of a "hierarchical code"
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct efficient soft-output decoders for the surface code derived from the Minimum-Weight Perfect Matching and Union-Find decoders. We show that soft-output decoding can improve the performance of a "hierarchical code," a concatenated scheme in which the inner code is the surface code, and the outer code is a high-rate quantum low-density parity-check code. Alternatively, the soft-output decoding can improve the reliability of fault-tolerant circuit sampling by flagging those runs that should be discarded because the probability of a logical error is intolerably large.

Related papers

• Decoding across transversal Clifford gates in the surface code [0.7100520098029438]
  We show how one can decode across an arbitrary sequence of window gates for the unrotated surface code.<n>Our work highlights the complexity and interest in efficient decoding of fast logic for the surface code.
  arXiv  Detail & Related papers  (2025-05-19T18:00:02Z)
• 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)
• Optimal Decoder for the Error Correcting Parity Code [0.0]
  We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings.<n>For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes while yielding near-optimal decoding for intermediate code sizes.
  arXiv  Detail & Related papers  (2025-05-08T13:03:22Z)
• 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)
• Generalizing the matching decoder for the Chamon code [1.8416014644193066]
  We implement a matching decoder for a three-dimensional, non-CSS, low-density parity check code known as the Chamon code. 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 depolarising noise.
  arXiv  Detail & Related papers  (2024-11-05T19:00:12Z)
• Localized statistics decoding: A parallel decoding algorithm for quantum low-density parity-check codes [3.001631679133604]
  We introduce localized statistics decoding for arbitrary quantum low-density parity-check codes. Our decoder is more amenable to implementation on specialized hardware, positioning it as a promising candidate for decoding real-time syndromes from experiments.
  arXiv  Detail & Related papers  (2024-06-26T18:00:09Z)
• 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)
• 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)
• Modular decoding: parallelizable real-time decoding for quantum computers [55.41644538483948]
  Real-time quantum computation will require decoding algorithms capable of extracting logical outcomes from a stream of data generated by noisy quantum hardware. We propose modular decoding, an approach capable of addressing this challenge with minimal additional communication and without sacrificing decoding accuracy. We introduce the edge-vertex decomposition, a concrete instance of modular decoding for lattice-surgery style fault-tolerant blocks.
  arXiv  Detail & Related papers  (2023-03-08T19:26:10Z)
• 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)
• Adversarial Neural Networks for Error Correcting Codes [76.70040964453638]
  We introduce a general framework to boost the performance and applicability of machine learning (ML) models. We propose to combine ML decoders with a competing discriminator network that tries to distinguish between codewords and noisy words. Our framework is game-theoretic, motivated by generative adversarial networks (GANs)
  arXiv  Detail & Related papers  (2021-12-21T19:14:44Z)
• On Sparsifying Encoder Outputs in Sequence-to-Sequence Models [90.58793284654692]
  We take Transformer as the testbed and introduce a layer of gates in-between the encoder and the decoder. The gates are regularized using the expected value of the sparsity-inducing L0penalty. We investigate the effects of this sparsification on two machine translation and two summarization tasks.
  arXiv  Detail & Related papers  (2020-04-24T16:57:52Z)
• Combining hard and soft decoders for hypergraph product codes [0.3326320568999944]
  Hypergraph product codes are constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF) This decoder displays sub-optimal performance in practice and requires very large error correcting codes to be effective. We present new hybrid decoders that combine the belief propagation (BP) algorithm with the SSF decoder.
  arXiv  Detail & Related papers  (2020-04-23T14:48:05Z)

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.