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Related papers: Generalized Concatenated Quantum Codes

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Codeword stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and non-additive quantum codes. Standard codeword stabilized quantum codes encode quantum information into…

Quantum Physics · Physics 2012-10-18 Jeonghwan Shin , Jun Heo , Todd A. Brun

Code concatenation combines two or more component codes to design larger codes with greater noise resilience. Introducing entanglement assistance to concatenated codes provides a further advantage in terms of improved error rates and…

Quantum Physics · Physics 2025-11-25 Nihar Ranjan Dash , Sanjoy Dutta , R. Srikanth , Subhashish Banerjee

Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, a new method for construct quantum…

Quantum Physics · Physics 2022-03-21 Tao Wang , Tongjiang Yan , Shiwen Sun

We first present a useful characterization of additive (stabilizer) quantum error-correcting codes. Then we present several examples of We first present a useful characterization of additive (stabilizer) quantum error--correcting codes.…

Quantum Physics · Physics 2007-05-23 Vwani P. Roychowdhury , Farrokh Vatan

One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…

Information Theory · Computer Science 2015-08-06 Tao Zhang , Gennian Ge

Protecting quantum information from the detrimental effects of decoherence and lack of precise quantum control is a central challenge that must be overcome if a large robust quantum computer is to be constructed. The traditional approach to…

Quantum Physics · Physics 2009-11-13 D. Bacon

Fault-tolerant capacities quantify the ability of a quantum channel to reliably transmit information when every component of the encoding and decoding procedure is noisy. Earlier work analyzed achievable communication rates under such noise…

Quantum Physics · Physics 2026-02-11 Paula Belzig , Hayata Yamasaki

Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the…

Quantum Physics · Physics 2015-05-30 Jeonghwan Shin , Jun Heo , Todd A. Brun

We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them…

Quantum Physics · Physics 2009-11-13 Zhuo Li , Li-Juan Xing , Xin-Mei Wang

We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding…

Information Theory · Computer Science 2010-06-02 G. O. Santos , F. M. Assis , A. F. Lima

We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…

Quantum Physics · Physics 2007-05-23 H. Ollivier , J. -P. Tillich

Hybrid codes simultaneously encode both quantum and classical information into physical qubits. We give several general results about hybrid codes, most notably that the quantum codes comprising a genuine hybrid code must be impure and that…

Quantum Physics · Physics 2020-09-11 Andrew Nemec , Andreas Klappenecker

Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…

Quantum Physics · Physics 2026-04-29 Nicholas J. C. Papadopoulos , Ramin Ayanzadeh

We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…

Quantum Physics · Physics 2009-07-30 Peter W. Shor , Graeme Smith , John A. Smolin , Bei Zeng

We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an…

Quantum Physics · Physics 2022-05-03 Christophe Vuillot , Nikolas P. Breuckmann

One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…

Quantum Physics · Physics 2007-07-13 Avanti Ketkar , Andreas Klappenecker , Santosh Kumar , Pradeep Kiran Sarvepalli

In this work, we present a generalization of the recently proposed quantum Tanner codes by Leverrier and Z\'emor, which contains a construction of asymptotically good quantum LDPC codes. Quantum Tanner codes have so far been constructed…

Information Theory · Computer Science 2024-08-19 Olai Å. Mostad , Eirik Rosnes , Hsuan-Yin Lin

We introduce generalized spatially coupled parallel concatenated codes (GSC-PCCs), a class of spatially coupled turbo-like codes obtained by coupling parallel concatenated codes (PCCs) with a fraction of information bits repeated before the…

Information Theory · Computer Science 2021-05-04 Min Qiu , Xiaowei Wu , Jinhong Yuan , Alexandre Graell i Amat

We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…

Quantum Physics · Physics 2009-11-10 H. Ollivier , J. -P. Tillich

We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of…

Combinatorics · Mathematics 2017-03-20 J. Borges , J. Rifà , V. Zinoviev