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Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. Quantum LRCs have very recently been introduced for their potential…

Information Theory · Computer Science 2023-12-19 Gaojun Luo , Bocong Chen , Martianus Frederic Ezerman , San Ling

We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…

Quantum Physics · Physics 2009-05-24 Markus Grassl , Peter Shor , Graeme Smith , John Smolin , Bei Zeng

Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…

Quantum Physics · Physics 2015-06-05 Zhuo Wang , Sixia Yu , Heng Fan , C. H. Oh

We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite…

We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes,…

Quantum Physics · Physics 2025-10-21 Matthew B. Hastings

Quantum error correction codes (QECCs) are critical for realizing reliable quantum computing by protecting fragile quantum states against noise and errors. However, limited research has analyzed the noise resilience of QECCs to help select…

Quantum Physics · Physics 2025-04-22 Avimita Chatterjee , Subrata Das , Swaroop Ghosh

As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and…

Information Theory · Computer Science 2007-07-16 Eric Zhi Chen

We introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes. We apply this framework to bosonic coding, obtaining multimode extensions of the cat…

Quantum Physics · Physics 2025-10-14 Shubham P. Jain , Joseph T. Iosue , Alexander Barg , Victor V. Albert

This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…

Quantum Physics · Physics 2007-05-23 Hsun-Hsien Chang

Locating the boundaries of consecutive blocks of quantum information is a fundamental building block for advanced quantum computation and quantum communication systems. We develop a coding theoretic method for properly locating boundaries…

Quantum Physics · Physics 2013-03-01 Yuichiro Fujiwara

Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…

Quantum Physics · Physics 2009-10-31 H. F. Chau

In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…

Quantum Physics · Physics 2012-02-28 Ching-Yi Lai , Chung-Chin Lu

Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…

Quantum Physics · Physics 2009-04-17 Daniel Gottesman

We introduce the concept of quantum locally recoverable codes (qLRCs) with intersecting recovery sets. We derive a singleton-like bound for these codes by leveraging the additional information provided by the intersecting recovery sets.…

Quantum Physics · Physics 2025-01-20 Kaifeng Bu , Weichen Gu , Xiang Li

One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing on QC codes…

Information Theory · Computer Science 2021-08-17 Dev Akre , Nuh Aydin , Matthew J. Harrington , Saurav R. Pandey

We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.

Quantum Physics · Physics 2007-05-23 D. Schlingemann

Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…

Quantum Physics · Physics 2025-01-10 Lane G. Gunderman

Practical applications of quantum computing depend on fault-tolerant devices with error correction. Today, the most promising approach is a class of error-correcting codes called surface codes. We study the problem of compiling quantum…

Quantum Physics · Physics 2025-04-29 Abtin Molavi , Amanda Xu , Swamit Tannu , Aws Albarghouthi

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…

Quantum Physics · Physics 2009-02-19 Andrew Cross , Graeme Smith , John A. Smolin , Bei Zeng

We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…

Quantum Physics · Physics 2016-11-17 David J. C. MacKay , Graeme Mitchison , Paul L. McFadden