Data-driven decoding of quantum error correcting codes using graph neural networks

• URL: http://arxiv.org/abs/2307.01241v1
• Date: Mon, 3 Jul 2023 17:25:45 GMT
• Title: Data-driven decoding of quantum error correcting codes using graph neural networks
• Authors: Moritz Lange, Pontus Havstr\"om, Basudha Srivastava, Valdemar Bergentall, Karl Hammar, Olivia Heuts, Evert van Nieuwenburg, and Mats Granath
• Abstract summary: We explore a model-free, data-driven, approach to decoding, using a graph neural network (GNN) We show that the GNN-based decoder can outperform a matching decoder for circuit level noise on the surface code given only simulated data. The results show that a purely data-driven approach to decoding may be a viable future option for practical quantum error correction.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To leverage the full potential of quantum error-correcting stabilizer codes it is crucial to have an efficient and accurate decoder. Accurate, maximum likelihood, decoders are computationally very expensive whereas decoders based on more efficient algorithms give sub-optimal performance. In addition, the accuracy will depend on the quality of models and estimates of error rates for idling qubits, gates, measurements, and resets, and will typically assume symmetric error channels. In this work, instead, we explore a model-free, data-driven, approach to decoding, using a graph neural network (GNN). The decoding problem is formulated as a graph classification task in which a set of stabilizer measurements is mapped to an annotated detector graph for which the neural network predicts the most likely logical error class. We show that the GNN-based decoder can outperform a matching decoder for circuit level noise on the surface code given only simulated experimental data, even if the matching decoder is given full information of the underlying error model. Although training is computationally demanding, inference is fast and scales approximately linearly with the space-time volume of the code. We also find that we can use large, but more limited, datasets of real experimental data [Google Quantum AI, Nature {\bf 614}, 676 (2023)] for the repetition code, giving decoding accuracies that are on par with minimum weight perfect matching. The results show that a purely data-driven approach to decoding may be a viable future option for practical quantum error correction, which is competitive in terms of speed, accuracy, and versatility.

Related papers

• 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)
• qecGPT: decoding Quantum Error-correcting Codes with Generative Pre-trained Transformers [5.392298820599664]
  We propose a framework for decoding quantum error-correcting codes with generative modeling. We use autoregressive neural networks, specifically Transformers, to learn the joint probability of logical operators and syndromes. Our framework is general and can be applied to any error model and quantum codes with different topologies.
  arXiv  Detail & Related papers  (2023-07-18T07:34:02Z)
• Neural network decoder for near-term surface-code experiments [0.7100520098029438]
  Neural-network decoders can achieve a lower logical error rate compared to conventional decoders. These decoders require no prior information about the physical error rates, making them highly adaptable.
  arXiv  Detail & Related papers  (2023-07-06T20:31:25Z)
• 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)
• 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)
• A Practical and Scalable Decoder for Topological Quantum Error Correction with Digital Annealer [0.5658123802733283]
  We propose an efficient and scalable decoder for quantum error correction using Fujitsu Digital Annealer (DA) In particular, we implement the proposed DA decoder for the surface code and perform detailed numerical experiments for various code to see its performance and scalability. It is also shown that the DA decoder has advantages over the Union-Find (UF) decoder from a variety of perspectives including hardware implementation.
  arXiv  Detail & Related papers  (2022-03-29T07:48:51Z)
• 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)
• Error-rate-agnostic decoding of topological stabilizer codes [0.0]
  We develop a decoder that depends on the bias, i.e., the relative probability of phase-flip to bit-flip errors, but is agnostic to error rate. Our decoder is based on counting the number and effective weight of the most likely error chains in each equivalence class of a given syndrome.
  arXiv  Detail & Related papers  (2021-12-03T15:45:12Z)
• 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.