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In this article we study the role that quantum resources play in quantum error correction assisted quantum metrology (QECQM) schemes. We show that there exist classes of such problems where entanglement is not necessary to retrieve noise…

Quantum Physics · Physics 2019-08-21 K. C. Tan , S. Omkar , H. Jeong

We introduce a theory of quantum error correction (QEC) for a subclass of states within a larger Hilbert space. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords.…

Quantum Physics · Physics 2022-07-13 Maximilian Reichert , Louis W. Tessler , Marcel Bergmann , Peter van Loock , Tim Byrnes

Quantum error correction codes defined on hyperbolic lattices leverage the unique geometric properties of the hyperbolic space to enhance the performance of quantum error correction. By embedding qubits in hyperbolic lattices, these codes…

Quantum Physics · Physics 2026-04-07 Ahmed Adel Mahmoud , Kamal Mohamed Ali , Steven Rayan

In distributed quantum storage, physical qubits of a code will be stored across the network. When qubits in one of the nodes are lost i.e. when the node is erased, the remaining nodes need to communicate with a new node to replace the lost…

Quantum Physics · Physics 2025-05-27 Kaushik Senthoor

We introduce the notion of entanglement of subspaces as a measure that quantify the entanglement of bipartite states in a randomly selected subspace. We discuss its properties and in particular we show that for maximally entangled subspaces…

Quantum Physics · Physics 2011-11-09 Gilad Gour , Nolan R. Wallach

It is commonly believed that logical states of quantum error-correcting codes have to be highly entangled such that codes capable of correcting more errors require more entanglement to encode a qubit. Here, we show that the validity of this…

Quantum Physics · Physics 2025-06-16 Sergey Bravyi , Dongjin Lee , Zhi Li , Beni Yoshida

Quantum Error Correction Codes (QECCs) are pivotal in advancing quantum computing by protecting quantum states against the adverse effects of noise and errors. With a variety of QECCs developed, including new developments and modifications…

Quantum Physics · Physics 2025-01-30 Avimita Chatterjee , Swaroop Ghosh

In this paper we extend to asymmetric quantum error-correcting codes (AQECC) the construction methods, namely: puncturing, extending, expanding, direct sum and the (u|u + v) construction. By applying these methods, several families of…

Quantum Physics · Physics 2013-03-04 Giuliano G. La Guardia

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we…

Information Theory · Computer Science 2014-05-22 Liqi Wang , Shixin Zhu

This paper generalizes results in noncoherent space-time block code (STBC) design based on quantum error correction (QEC) to new antenna configurations. Previous work proposed QEC-inspired STBCs for antenna geometries where the number of…

Signal Processing · Electrical Eng. & Systems 2026-01-27 S. Andrew Lanham , Eli Bradley , Brian R. La Cour

Conjucyclic codes are part of a family of codes that includes cyclic, constacyclic, and quasi-cyclic codes, among others. Despite their importance in quantum error correction, they have not received much attention in the literature. This…

Information Theory · Computer Science 2023-09-06 Md Ajaharul Hossain , Ramakrishna Bandi

Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…

Quantum Physics · Physics 2007-06-26 Andrew S. Fletcher

Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a…

Quantum Physics · Physics 2019-10-23 Rounak Mundra , Dhrumil Patel , Indranil Chakrabarty , Nirman Ganguly , Sourav Chatterjee

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

In this work, we introduce a method to construct fault-tolerant measurement-based quantum computation (MBQC) architectures and numerically estimate their performance over various types of networks. A possible application of such a paradigm…

Quantum Physics · Physics 2025-05-07 Yves van Montfort , Sébastian de Bone , David Elkouss

We present two methods for the construction of quantum circuits for quantum error-correcting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC…

Quantum Physics · Physics 2023-11-27 Markus Grassl , Martin Roetteler , Thomas Beth

By interpreting the well-known, qualitative criteria for the existence of quantum error correction (QEC) codes by Knill and Laflamme from a quantitative perspective, we propose a figure of merit for assessing a QEC scheme based on the…

Quantum Physics · Physics 2013-03-05 Ricardo Wickert , Peter van Loock

Quantum computing holds transformative potential for various fields, yet its practical application is hindered by the susceptibility to errors. This study makes a pioneering contribution by applying quantum error correction codes (QECCs)…

Quantum Physics · Physics 2024-04-23 Avimita Chatterjee , Debarshi Kundu , Swaroop Ghosh

Quantum error correction (QEC) codes are necessary to fault-tolerantly operate quantum computers. However, every such code is inherently limited by its inability to detect logical errors. Here, we propose and implement a method that…

Linear programming approaches have been applied to derive upper bounds on the size of classical codes and quantum codes. In this paper, we derive similar results for general quantum codes with entanglement assistance, including nonadditive…

Information Theory · Computer Science 2018-01-16 Ching-Yi Lai , Alexei Ashikhmin