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Universal Framework for Quantum Error-Correcting Codes [PDF]
Entropy, 2021 We present a universal framework for quantum error-correcting codes, i.e., a framework that applies to the most general quantum error-correcting codes. This framework is based on the group algebra, an algebraic notation associated with nice error bases of quantum systems.
Lijuan Xing, Zhuo Li
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Construction of Binary Quantum Error-Correcting Codes from Orthogonal Array
Entropy, 2022 By using difference schemes, orthogonal partitions and a replacement method, some new methods to construct pure quantum error-correcting codes are provided from orthogonal arrays.
Shanqi Pang, Hanxiao Xu
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Quantum Error-Correcting Codes Based on Orthogonal Arrays
Entropy, 2023 In this paper, by using the Hamming distance, we establish a relation between quantum error-correcting codes ((N,K,d+1))s and orthogonal arrays with orthogonal partitions.
Shanqi Pang
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QUANTUM ERROR-CORRECTING CODES
Mathematical Aspects of Quantum Computing 2007, 2008exaly +5 more sources
Perfect Quantum Error Correcting Code
Physical Review Letters, 1996We present a quantum error correction code which protects a qubit of information against general one qubit errors. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state $|0〉$
, Laflamme, , Miquel, , Paz, , Zurek
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Classic and Quantum Error Correcting Codes
2008Algebraic methods play an important role in coding theory. For instance, there are many connections between codes and groups. In this paper we will present two results that show different applications of algebraic methods in coding theory. One of them refers to the classical context and another one to the quantum error correcting theory.
Santos González +2 more
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Quantum Error Correcting Codes
2020In this chapter we introduce the concept of quantum error-correcting codes and show several examples chronologically. This chapter is fundamental for the development of this work, since the main aim of this book is to present several types of different constructions of quantum block and convolutional codes, as well as constructions of asymmetric ...
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Comment on “Quantum convolutional error-correcting codes”
Physical Review A, 2005In this Comment we present a counterexample to theorems 2 and 3 from Chau [Phys. Rev. A 58, 905 (1998)] regarding quantum convolutional codes.
De Almeida, ACA, Palazzo, R, Chau, HF
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Quantum Error-Correcting Codes
2019Any quantum system inevitably interacts with the environment which causes decoherence. While the environment is generally inaccessible, can we protect our system against noise to maintain its quantum coherence? One technique developed in quantum information science, called the quantum error-correcting codes, does the job.
Bei Zeng +3 more
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Quantum Error-Correcting Codes
2001So far we have been dealing with a highly idealized situation in which physical states have been assumed to be stable and independent of time and in which unitary transformations on these states can be effected in a reliable fashion. The real situation is considerably more complicated and requires a model for the dynamics of a quantum system.
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