Analysis of the Error-Correcting Radius of a Renormalisation Decoder for Kitaev's Toric Code

• URL: http://arxiv.org/abs/2309.12165v1
• Date: Thu, 21 Sep 2023 15:23:41 GMT
• Title: Analysis of the Error-Correcting Radius of a Renormalisation Decoder for Kitaev's Toric Code
• Authors: Wouter Rozendaal and Gilles Z\'emor
• Abstract summary: Kitaev's toric code is arguably the most studied quantum code. Renormalisation decoders exhibit one of the best trade-offs between efficiency and speed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Kitaev's toric code is arguably the most studied quantum code and is expected to be implemented in future generations of quantum computers. The renormalisation decoders introduced by Duclos-Cianci and Poulin exhibit one of the best trade-offs between efficiency and speed, but one question that was left open is how they handle worst-case or adversarial errors, i.e. what is the order of magnitude of the smallest weight of an error pattern that will be wrongly decoded. We initiate such a study involving a simple hard-decision and deterministic version of a renormalisation decoder. We exhibit an uncorrectable error pattern whose weight scales like $d^{1/2}$ and prove that the decoder corrects all error patterns of weight less than $\frac{5}{6} d^{\log_{2}(6/5)}$, where $d$ is the minimum distance of the toric code.

Related papers

• Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction [44.698141103370546]
  We introduce a universal decoder based on linear attention sequence modeling and graph neural network. Our experiments demonstrate that this decoder outperforms specialized algorithms in both accuracy and speed.
  arXiv  Detail & Related papers  (2025-02-27T10:56:53Z)
• Demonstrating dynamic surface codes [138.1740645504286]
  We experimentally demonstrate three time-dynamic implementations of the surface code. First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three. Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors. Third, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead.
  arXiv  Detail & Related papers  (2024-12-18T21:56:50Z)
• A blindness property of the Min-Sum decoding for the toric code [3.543432625843538]
  Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation. Recent efforts have been devoted to improving the error correction performance of the toric code under message-passing decoding.
  arXiv  Detail & Related papers  (2024-06-21T08:28:31Z)
• The closed-branch decoder for quantum LDPC codes [0.0]
  Real-time decoding is a necessity for implementing arbitrary quantum computations on the logical level. We present a new decoder for Quantum Low Density Parity Check (QLDPC) codes, named the closed-branch decoder.
  arXiv  Detail & Related papers  (2024-02-02T16:22:32Z)
• Bit-flipping Decoder Failure Rate Estimation for (v,w)-regular Codes [84.0257274213152]
  We propose a new technique to provide accurate estimates of the DFR of a two-iterations (parallel) bit flipping decoder. 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)
• 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)
• 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)
• Local Probabilistic Decoding of a Quantum Code [0.0]
  flip is an extremely simple and maximally local classical decoder. Lowest-weight uncorrectable errors for this decoder are closer to correctable errors than to other uncorrectable errors. Introducing randomness into the decoder can allow it to correct these "uncorrectable" errors with finite probability.
  arXiv  Detail & Related papers  (2022-12-14T02:44:26Z)
• 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)
• Exponential suppression of bit or phase flip errors with repetitive error correction [56.362599585843085]
  State-of-the-art quantum platforms typically have physical error rates near $10-3$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits. We implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors.
  arXiv  Detail & Related papers  (2021-02-11T17:11:20Z)
• Correcting spanning errors with a fractal code [7.6146285961466]
  We propose an efficient decoder for the Fibonacci code'; a two-dimensional classical code that mimics the fractal nature of the cubic code. We perform numerical experiments that show our decoder is robust to one-dimensional, correlated errors.
  arXiv  Detail & Related papers  (2020-02-26T19:00:06Z)

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.