Toward a Union-Find decoder for quantum LDPC codes

• URL: http://arxiv.org/abs/2103.08049v1
• Date: Sun, 14 Mar 2021 21:55:48 GMT
• Title: Toward a Union-Find decoder for quantum LDPC codes
• Authors: Nicolas Delfosse, Vivien Londe and Michael Beverland
• Abstract summary: We propose a generalization of the Union-Find decoder as adecoder for quantum LDPC codes. We prove that this decoder corrects all errors with weight up to Analpha for some A, alpha > 0 for different classes of quantum LDPC codes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum LDPC codes are a promising direction for low overhead quantum computing. In this paper, we propose a generalization of the Union-Find decoder as adecoder for quantum LDPC codes. We prove that this decoder corrects all errors with weight up to An^{\alpha} for some A, {\alpha} > 0 for different classes of quantum LDPC codes such as toric codes and hyperbolic codes in any dimension D \geq 3 and quantum expander codes. To prove this result, we introduce a notion of covering radius which measures the spread of an error from its syndrome. We believe this notion could find application beyond the decoding problem. We also perform numerical simulations, which show that our Union-Find decoder outperforms the belief propagation decoder in the low error rate regime in the case of a quantum LDPC code with length 3600.

Related papers

• List Decodable Quantum LDPC Codes [49.2205789216734]
  We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff. We get efficiently list decodable QLDPC codes with unique decoders.
  arXiv  Detail & Related papers  (2024-11-06T23:08:55Z)
• Almost Linear Decoder for Optimal Geometrically Local Quantum Codes [8.837439668920288]
  We show how to achieve geometrically local codes that maximize both the dimension and the distance, as well as the energy barrier of the code. This provides the first decoder for an optimal 3D geometrically local code.
  arXiv  Detail & Related papers  (2024-11-05T09:15:06Z)
• Decoding Quantum LDPC Codes Using Graph Neural Networks [52.19575718707659]
  We propose a novel decoding method for Quantum Low-Density Parity-Check (QLDPC) codes based on Graph Neural Networks (GNNs) The proposed GNN-based QLDPC decoder exploits the sparse graph structure of QLDPC codes and can be implemented as a message-passing decoding algorithm.
  arXiv  Detail & Related papers  (2024-08-09T16:47:49Z)
• Many-hypercube codes: High-rate quantum error-correcting codes for high-performance fault-tolerant quantum computing [0.0]
  We propose high-rate small-size quantum error-detecting codes as a new family of high-rate quantum codes. Their simple structure allows for a geometrical interpretation using hypercubes corresponding to logical qubits. We achieve high error thresholds even in a circuit-level noise model.
  arXiv  Detail & Related papers  (2024-03-24T07:46:26Z)
• Small Quantum Codes from Algebraic Extensions of Generalized Bicycle Codes [4.299840769087443]
  Quantum LDPC codes range from the surface code, which has a vanishing encoding rate, to very promising codes with constant encoding rate and linear distance. We devise small quantum codes that are inspired by a subset of quantum LDPC codes, known as generalized bicycle (GB) codes.
  arXiv  Detail & Related papers  (2024-01-15T10:38:13Z)
• Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes with Overcomplete Check Matrices [45.997444794696676]
  Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. We first propose to decode QLDPC codes with a belief propagation (BP) decoder operating on overcomplete check matrices. We extend the neural BP (NBP) decoder, which was originally studied for suboptimal binary BP decoding of QLPDC codes, to quaternary BP decoders.
  arXiv  Detail & Related papers  (2023-08-16T08:24:06Z)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [51.9157257936691]
  homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code. We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
  arXiv  Detail & Related papers  (2023-03-24T00:29:15Z)
• 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)
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders [67.12391801199688]
  We investigate dense coding by imposing various locality restrictions to our decoder. In this task, the sender Alice and the receiver Bob share an entangled state.
  arXiv  Detail & Related papers  (2021-09-26T07:29:54Z)
• Connectivity constrains quantum codes [0.06091702876917279]
  We study the limitations of quantum LDPC codes associated with local graphs in $D$-dimensional hyperbolic space. We find that unless the connectivity graph contains an expander, the code is severely limited. As an application, we present novel bounds on quantum LDPC codes associated with local graphs in $D$-dimensional hyperbolic space.
  arXiv  Detail & Related papers  (2021-06-01T20:03:16Z)

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.