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Entanglement-assisted quantum error correcting codes (EAQECCs) can be derived from arbitrary classical linear codes. However, it is a very difficult task to determine the number of entangled states required. In this work, using the method…

Information Theory · Computer Science 2020-04-22 Liangdong Lu , Wenping Ma , Luobin Guo

Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…

Quantum Physics · Physics 2024-03-29 Zipeng Wu , Song Cheng , Bei Zeng

$k$-uniform states are valuable resources in quantum information, enabling tasks such as teleportation, error correction, and accelerated quantum simulations. The practical realization of $k$-uniform states, at scale, faces major obstacles:…

Quantum Physics · Physics 2025-10-14 Shayan Majidy , Dominik Hangleiter , Michael J. Gullans

We design a series of quantum circuits that generate absolute maximally entangled (AME) states to benchmark a quantum computer. A relation between graph states and AME states can be exploited to optimize the structure of the circuits and…

Quantum Physics · Physics 2019-09-02 Alba Cervera-Lierta , José Ignacio Latorre , Dardo Goyeneche

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

Entanglement-assisted quantum error-correcting (EAQEC) codes make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQEC code from any classical linear code,…

Information Theory · Computer Science 2020-03-03 Peng Hu , Xiusheng Liu

We present a general framework of quantum error-correcting codes (QECCs) as a subspace of a complex Hilbert space and the corresponding error models. Then we illustrate how QECCs can be constructed using techniques from algebraic coding…

Information Theory · Computer Science 2022-03-08 Markus Grassl

By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality…

Information Theory · Computer Science 2024-03-19 Xiujing Zheng , Liqi Wang , Shixin Zhu

Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…

Quantum Physics · Physics 2015-03-10 Zunaira Babar , Panagiotis Botsinis , Dimitrios Alanis , Soon Xin Ng , Lajos Hanzo

We show how to explicitly construct an $O(nd)$ size and constant quantum depth circuit which encodes any given $n$-qubit stabilizer code with $d$ generators. Our construction is derived using the graphic description for stabilizer codes and…

Quantum Physics · Physics 2008-08-18 Wei Huang , Zhaohui Wei

For every stabiliser $N$-qudit absolutely maximally entangled state, we present a method for determining the stabiliser generators and logical operators of a corresponding quantum error correction code. These codes encode $k$ qudits into…

Quantum Physics · Physics 2020-04-07 Paweł Mazurek , Máté Farkas , Andrzej Grudka , Michał Horodecki , Michał Studziński

Consider a stabilizer state on $n$ qudits, each of dimension $D$ with $D$ being a prime or a squarefree integer, divided into three mutually disjoint sets or parts. Generalizing a result of Bravyi et al. [J. Math. Phys. \textbf{47}, 062106…

Quantum Physics · Physics 2011-12-05 Shiang Yong Looi , Robert B. Griffiths

Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…

Quantum Physics · Physics 2019-09-17 Fernando G. S. L. Brandao , Elizabeth Crosson , M. Burak Şahinoğlu , John Bowen

Up to now every good quantum error-correcting code discovered has had the structure of an eigenspace of an Abelian group generated by tensor products of Pauli matrices; such codes are known as stabilizer or additive codes. In this letter we…

Quantum Physics · Physics 2009-01-23 Eric M. Rains , R. H. Hardin , Peter W. Shor , N. J. A. Sloane

Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the…

Quantum Physics · Physics 2009-11-07 B. C. Travaglione , G. J. Milburn

Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…

Emerging Technologies · Computer Science 2013-08-09 Hector J. Garcia , Igor L. Markov , Andrew W. Cross

In this article, we present the unbalanced quantum error correcting codes(one-party-QECC), a novel idea for correcting unbalanced quantum errors. In some quantum communication tasks using entangled pairs, the error distributions between two…

Quantum Physics · Physics 2007-05-23 Kai Wen , Gui Lu Long

Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing entanglement-assisted quantum maximum distance separable…

Information Theory · Computer Science 2020-09-17 Wan Jiang , Shixin Zhu , Xiaojing Chen

Quantum state preparation is a fundamental component of quantum algorithms, particularly in quantum machine learning and data processing, where classical data must be encoded efficiently into quantum states. Existing amplitude encoding…

Quantum Physics · Physics 2026-02-11 Carsten Blank , Israel F. Araujo

Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…

Quantum Physics · Physics 2007-05-23 Daniel Gottesman