New optimal asymmetric quantum codes and quantum convolutional codes derived from constacyclic codes

Chen, Jianzhang; Chen, Youqin; Huang, Yuanyuan; Feng, Chunhui

doi:10.1007/s11128-018-2156-7

Cited by 15 publications

(7 citation statements)

References 43 publications

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“…There are many works related to the control of quantum computing errors, in addition to those already mentioned above. General studies and surveys on the subject [20,21,22,23,24,25,26,27], about the quantum computation threshold theorem [28,29,30,31], quantum error correction codes [32,33,34,35], concatenated quantum error correction codes [36,37] and articles related to topological quantum codes [38,39]. Lately, quantum computing error control has focused on both coherent errors [40,41] and cross-talk errors [42,43].…”

Section: Introductionmentioning

confidence: 99%

Quantum codes do not fix isotropic errors

Lacalle

Coronado

Oliveira

2021

Quantum Inf Process

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Given an m−qubit Φ0 and an (n, m)−quantum code C, let Φ be the n−qubit that results from the C−encoding of Φ0. Suppose that the state Φ is affected by an isotropic error (decoherence), becoming Ψ, and that the corrector circuit of C is applied to Ψ, obtaining the quantum state Φ. Alternatively, we analyze the effect of the isotropic error without using the quantum code C. In this case the error transforms Φ0 into Ψ0. Assuming that the correction circuit does not introduce new errors and that it does not increase the execution time, we compare the fidelity of Ψ, Φ and Ψ0 with the aim of analyzing the power of quantum codes to control isotropic errors. We prove that F (Ψ0) ≥ F ( Φ) ≥ F (Ψ). Therefore the best option to optimize fidelity against isotropic errors is not to use quantum codes.

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Section: Introductionmentioning

confidence: 99%

Quantum codes do not fix isotropic errors

Lacalle

Coronado

Oliveira

2021

Quantum Inf Process

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“…, where q is an odd prime power of the form 10hm + 10ht, m ≥ 2 is an even, both h and t are odd with 10h = t 2 + 1 and t ≥ 3, both δ 1 and δ 2 are integers such that 0 ≤ δ 1 ≤ q -10ht 20h and q -3 2 ≤ δ 2 ≤ q -3 2 + Qδ 1 [10] .…”

Section: )mentioning

confidence: 99%

“…La Guardia [6,7] utilized classical Bose-Chaudhuri-Hocquenghem (BCH) codes to construct new classes of AQEC codes. Later, several classes of optimal AQEC codes have been constructed [8][9][10][11][12][13][14][15] . Chen et al [8] studied optimal AQEC codes by using negacyclic codes.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Asymmetric Quantum Codes from the Euclidean Sums of Linear Codes

XU,

LIU

2024

Wuhan Univ. J. Nat. Sci.

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In this paper, we first give the definition of the Euclidean sums of linear codes, and prove that the Euclidean sums of linear codes are Euclidean dual-containing. Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes, and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields. Moreover, these optimal asymmetric quantum error-correcting codes constructed in this paper are different from the ones in the literature.

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“…In the quantum information and quantum computing, an important subject is to constuct some good quantum error-correcting codes (quantum codes for short) [3], [5], [7], [8], [15], [18], [30], [31], [35]- [37], [42]. Let q be a prime power, a q-ary quantum code of length n can be denoted as [[n, k, d]] q , where k represents the size of q k that is a q k -dimensional subspace of the q n -dimensional Hilbert space and d is the minimum distance.…”

Section: Introductionmentioning

confidence: 99%

Some New Classes of Entanglement-Assisted Quantum MDS Codes Derived From Constacyclic Codes

Chen

Feng

et al. 2019

IEEE Access

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Although quantum maximal-distance-separable (MDS) codes that satisfy the quantum singleton bound have become an important research topic in the quantum coding theory, it is not an easy task to search for quantum MDS codes with the minimum distance that is larger than (q/2) + 1. The pre-shared entanglement between the sender and the receiver can improve the minimum distance of quantum MDS codes such that the minimum distance of some constructed codes achieves (q/2) + 1 or exceeds (q/2) + 1. Meanwhile, how to determine the required number of maximally entangled states to make the minimum distance of quantum MDS codes larger than (q/2) + 1 is an interesting problem in the quantum coding theory. In this paper, we utilize the decomposition of the defining set and q 2-cyclotomic cosets of constacyclic codes with the form q = αm + t or q = αm + α − t and n = (q 2 + 1/α) to construct some new families of entanglement-assisted quantum MDS codes that satisfy the entanglement-assisted quantum singleton bound, where q is an odd prime power and m is a positive integer, while both α and t are positive integers such that α = t 2 + 1. The parameters of these codes constructed in this paper are more general compared with the ones in the literature. Moreover, the minimum distance of some codes in this paper is larger than (q/2) + 1 or q + 1. INDEX TERMS Entanglement-assisted quantum codes, constacyclic codes, maximal-distance-separable (MDS) codes.

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New optimal asymmetric quantum codes and quantum convolutional codes derived from constacyclic codes

Cited by 15 publications

References 43 publications

Quantum codes do not fix isotropic errors

Quantum codes do not fix isotropic errors

Optimal Asymmetric Quantum Codes from the Euclidean Sums of Linear Codes

Some New Classes of Entanglement-Assisted Quantum MDS Codes Derived From Constacyclic Codes

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