Fault-tolerant noise guessing decoding of quantum random codes

• URL: http://arxiv.org/abs/2407.01658v1
• Date: Mon, 1 Jul 2024 17:54:23 GMT
• Title: Fault-tolerant noise guessing decoding of quantum random codes
• Authors: Diogo Cruz, Francisco A. Monteiro, André Roque, Bruno C. Coutinho,
• Abstract summary: We present a new decoder for quantum random linear codes (QRLCs) capable of dealing with imperfect decoding operations. We analyze the fault-tolerant characteristics of QRLCs with a new noise-guessing decoding technique.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work addresses the open question of implementing fault-tolerant QRLCs with feasible computational overhead. We present a new decoder for quantum random linear codes (QRLCs) capable of dealing with imperfect decoding operations. A first approach, introduced by Cruz et al., only considered channel errors, and perfect gates at the decoder. Here, we analyze the fault-tolerant characteristics of QRLCs with a new noise-guessing decoding technique, when considering preparation, measurement, and gate errors in the syndrome extraction procedure, while also accounting for error degeneracy. Our findings indicate a threshold error rate ($\pth$) of approximately $\pnum$ in the asymptotic limit, while considering realistic noise levels in the mentioned physical procedures.

Related papers

• Analysis of Maximum Threshold and Quantum Security for Fault-Tolerant Encoding and Decoding Scheme Base on Steane Code [10.853582091917236]
  The original Steane code is not fault-tolerant because the CNOT gates in an encoded block may cause error propagation. We first propose a fault-tolerant encoding and decoding scheme, which analyzes all possible errors caused by each quantum gate in an error-correction period. We then provide the fault-tolerant scheme of the universal quantum gate set, including fault-tolerant preparation and verification of ancillary states.
  arXiv  Detail & Related papers  (2024-03-07T07:46:03Z)
• Fault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes [0.24578723416255752]
  Low-depth random circuit codes possess many desirable properties for quantum error correction. We design a fault-tolerant distillation protocol for preparing encoded states of one-dimensional random circuit codes. We show through numerical simulations that our protocol can correct erasure errors up to an error rate of $2%$.
  arXiv  Detail & Related papers  (2023-11-29T19:00:00Z)
• 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)
• Minimizing readout-induced noise for early fault-tolerant quantum computers [0.0]
  We present a different method for syndrome extraction, namely Generalized Syndrome Measurement. We can detect the error in the logical state with minimized readout-induced noise. We numerically analyze the performance of our protocol using Iceberg code and Steane code.
  arXiv  Detail & Related papers  (2023-04-23T04:16:26Z)
• 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)
• 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)
• Exact performance of the five-qubit code with coherent errors [0.0]
  We obtain explicit process matrix of the coding maps with a unital error channel for the five-qubit code. We analytically show how the code affects the average gate infidelity and diamond distance of the error channels.
  arXiv  Detail & Related papers  (2022-03-03T13:28:59Z)
• 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)
• Cellular automaton decoders for topological quantum codes with noisy measurements and beyond [68.8204255655161]
  We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, we focus on the three-dimensional (3D) toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model.
  arXiv  Detail & Related papers  (2020-04-15T18:00:01Z)

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.