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Related papers: Fast Decoders for Topological Quantum Codes

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Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these…

Quantum Physics · Physics 2021-01-12 Ryan Sweke , Markus S. Kesselring , Evert P. L. van Nieuwenburg , Jens Eisert

We introduce a family of 2D topological subsystem quantum error-correcting codes. The gauge group is generated by 2-local Pauli operators, so that 2-local measurements are enough to recover the error syndrome. We study the computational…

Quantum Physics · Physics 2010-03-04 H. Bombin

Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…

Quantum Physics · Physics 2025-03-28 Hanyan Cao , Feng Pan , Dongyang Feng , Yijia Wang , Pan Zhang

In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted…

Information Theory · Computer Science 2014-03-05 J. Li , R. C. de Lamare , H. Wymeersch

Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…

Quantum Physics · Physics 2017-04-14 Isaac H. Kim , Michael J. Kastoryano

We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight…

Quantum Physics · Physics 2022-10-26 Anthony Leverrier , Gilles Zémor

Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…

Quantum Physics · Physics 2024-02-02 Yugo Takada , Yusaku Takeuchi , Keisuke Fujii

Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the…

Quantum Physics · Physics 2026-03-24 Luca Menti , Francisco Lázaro

We explain an algorithm that approximately but efficiently assesses particular parity-check error-correcting codes of large, but finite, blocklength. This algorithm is based on the ``renormalization-group'' approach from physics: the idea…

Condensed Matter · Physics 2007-05-23 Jonathan Yedidia , Jean-Philippe Bouchaud

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…

Quantum Physics · Physics 2025-08-08 Shouzhen Gu , Mehdi Soleimanifar

Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…

Quantum Physics · Physics 2025-05-20 Oliver Weissl , Evgenii Egorov

We show that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes constructed from the hypergraph product. To this end, we run numerical simulations of the…

Quantum Physics · Physics 2021-01-04 Joschka Roffe , David R. White , Simon Burton , Earl T. Campbell

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

Computational Engineering, Finance, and Science · Computer Science 2024-05-14 Gabriel Garayalde , Matteo Torzoni , Matteo Bruggi , Alberto Corigliano

Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…

Quantum Physics · Physics 2026-04-10 Andi Gu , J. Pablo Bonilla Ataides , Mikhail D. Lukin , Susanne F. Yelin

Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance. A natural question concerns the efficient decodability of these codes. In this paper, we present a linear…

Quantum Physics · Physics 2022-06-15 Shouzhen Gu , Christopher A. Pattison , Eugene Tang

Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…

Quantum Physics · Physics 2024-09-12 Ruihua Fan , Yimu Bao , Ehud Altman , Ashvin Vishwanath

A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…

Information Theory · Computer Science 2012-05-22 Dung Viet Nguyen , Bane Vasic , Michael W. Marcellin

Encoding and manipulation of quantum information by means of topological degrees of freedom provides a promising way to achieve natural fault-tolerance that is built-in at the physical level. We show that this topological approach to…

Quantum Physics · Physics 2009-11-07 Paolo Zanardi , Seth Lloyd

A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less…

Quantum Physics · Physics 2024-01-15 Weishun Zhong , Oles Shtanko , Ramis Movassagh

The rapid growth of digital data has heightened the demand for efficient lossless compression methods. However, existing algorithms exhibit trade-offs: some achieve high compression ratios, others excel in encoding or decoding speed, and…

Information Theory · Computer Science 2025-10-01 Md. Atiqur Rahman , MM Fazle Rabbi