Progressive-Proximity Bit-Flipping for Decoding Surface Codes

• URL: http://arxiv.org/abs/2402.15924v2
• Date: Sat, 24 Aug 2024 09:42:49 GMT
• Title: Progressive-Proximity Bit-Flipping for Decoding Surface Codes
• Authors: Michele Pacenti, Mark F. Flanagan, Dimitris Chytas, Bane Vasic,
• Abstract summary: Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation. Existing decoders often fall short of meeting requirements such as having low computational complexity. We propose a novel bit-flipping (BF) decoder tailored for toric and surface codes.
• Score: 8.971989179518214
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently remains a challenge: existing decoders often fall short of meeting requirements such as having low computational complexity (ideally linear in the code's blocklength), low decoding latency, and low power consumption. In this paper we propose a novel bit-flipping (BF) decoder tailored for toric and surface codes. We introduce the proximity vector as a heuristic metric for flipping bits, and we develop a new subroutine for correcting degenerate multiple errors on adjacent qubits. Our algorithm has quadratic complexity growth and it can be efficiently implemented as it does not require operations on dynamic memories, as do state-of-art decoding algorithms such as minimum weight perfect matching or union find. The proposed decoder shows a decoding threshold of 7.5% for the 2D toric code and 7% for the rotated planar code over the binary symmetric channel.

Related papers

• 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)
• Accelerating Error Correction Code Transformers [56.75773430667148]
  We introduce a novel acceleration method for transformer-based decoders. We achieve a 90% compression ratio and reduce arithmetic operation energy consumption by at least 224 times on modern hardware.
  arXiv  Detail & Related papers  (2024-10-08T11:07:55Z)
• Collective Bit Flipping-Based Decoding of Quantum LDPC Codes [0.6554326244334866]
  We improve both the error correction performance and decoding latency of variable degree-3 (dv-3) QLDPC codes under iterative decoding. Our decoding scheme is based on applying a modified version of bit flipping (BF) decoding, namely two-bit bit flipping (TBF) decoding.
  arXiv  Detail & Related papers  (2024-06-24T18:51:48Z)
• Learning Linear Block Error Correction Codes [62.25533750469467]
  We propose for the first time a unified encoder-decoder training of binary linear block codes. We also propose a novel Transformer model in which the self-attention masking is performed in a differentiable fashion for the efficient backpropagation of the code gradient.
  arXiv  Detail & Related papers  (2024-05-07T06:47:12Z)
• Measurement-free fault-tolerant logical zero-state encoding of the distance-three nine-qubit surface code in a one-dimensional qubit array [0.0]
  We propose an efficient encoding method for the distance-three, nine-qubit surface code and show its fault tolerance. We experimentally demonstrate the logical zero-state encoding of the surface code using a superconducting quantum computer on the cloud. We numerically show that fault-tolerant encoding of this large code can be achieved by appropriate error detection.
  arXiv  Detail & Related papers  (2023-03-30T08:13:56Z)
• 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)
• 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)
• Conservation laws and quantum error correction: towards a generalised matching decoder [2.1756081703276]
  We explore decoding algorithms for the surface code, a prototypical quantum low-density parity-check code. The decoder works by exploiting underlying structure that arises due to materialised symmetries among surface-code stabilizer elements. We propose a systematic way of constructing a minimum-weight perfect-matching decoder for codes with certain characteristic properties.
  arXiv  Detail & Related papers  (2022-07-13T18:00:00Z)
• 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)
• 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)
• Pruning Neural Belief Propagation Decoders [77.237958592189]
  We introduce a method to tailor an overcomplete parity-check matrix to (neural) BP decoding using machine learning. We achieve performance within 0.27 dB and 1.5 dB of the ML performance while reducing the complexity of the decoder.
  arXiv  Detail & Related papers  (2020-01-21T12:05:46Z)

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.