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Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome…

Quantum Physics · Physics 2023-02-06 Andrew Nemec

This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the…

Quantum Physics · Physics 2024-07-23 Dimiter Ostrev

In the previous research by Grassl, Huber and Winter, they proved a theorem which can make entanglement-assisted quantum error-correcting codes (EAQECC) from general quantum error-correcting codes (QECC). In this paper, we prove that the…

Quantum Physics · Physics 2022-05-30 Daiki Ueno , Ryutaroh Matsumoto

We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…

Quantum Physics · Physics 2007-09-13 Sixia Yu , Qing Chen , C. H. Oh

The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…

Quantum Physics · Physics 2007-05-23 Dave Bacon , Andrea Casaccino

We discuss a method to construct quantum codes correcting amplitude damping errors via code concatenation. The inner codes are chosen as asymmetric Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes correcting symmetric…

Quantum Physics · Physics 2016-10-31 Tyler Jackson , Markus Grassl , Bei Zeng

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

Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…

Quantum Physics · Physics 2024-02-15 Pejman Jouzdani , H. Arslan Hashim , Eduardo R. Mucciolo

We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…

Quantum Physics · Physics 2017-03-28 Dave Bacon , Steven T. Flammia , Aram W. Harrow , Jonathan Shi

We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…

Quantum Physics · Physics 2011-03-31 Runyao Duan , Markus Grassl , Zhengfeng Ji , Bei Zeng

Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…

Quantum Physics · Physics 2026-04-17 Nico Meyer , Christopher Mutschler , Dominik Seuß , Andreas Maier , Daniel D. Scherer

We introduce a Steane-like enlargement procedure for entanglement-assisted quantum error-correcting codes (EAQECCs) obtained by considering Euclidean inner product. We give formulae for the parameters of these enlarged codes and apply our…

Information Theory · Computer Science 2024-05-01 Carlos Galindo , Fernando Hernando , Ryutaroh Matsumoto

One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we propose a class of 2-generator quasi-cyclic codes and study their applications in the…

Information Theory · Computer Science 2022-10-18 Chaofeng Guan , Ruihu Li , Liangdong Lu , Yang Liu , Hao Song

A major difficulty in quantum computation is the ability to implement fault tolerant computations, protecting information against undesired interactions with the environment. Stabiliser codes were introduced as a means to protect…

Quantum Physics · Physics 2025-12-17 Simeon Ball , Raven Zhang

In this paper, a construction of a pair of "regular" quasi-cyclic LDPC codes as ingredient codes for a quantum error-correcting code is proposed. That is, we find quantum regular LDPC codes with various weight distributions. Furthermore our…

Quantum Physics · Physics 2016-11-18 Manabu Hagiwara , Hideki Imai

We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…

Quantum Physics · Physics 2009-10-30 Richard Cleve

Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have…

We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as…

Information Theory · Computer Science 2021-01-29 Carlos Galindo , Fernando Hernando , Ryutaroh Matsumoto , Diego Ruano

We present a protocol for generating entanglement over long distances in a two-dimensional quantum network based on the surface error-correction code. This protocol requires a fixed number of quantum memories at each node of the network and…

Quantum Physics · Physics 2012-07-02 Ying Li , Daniel Cavalcanti , Leong Chuan Kwek

Additive codes and some nonadditive codes use the single and multiple invariant subspaces of the stabilizer G, respectively, to construct quantum codes, so the selection of the invariant subspaces is a key problem. In this paper, I provide…

Quantum Physics · Physics 2024-09-09 Jing-Lei Xia