Entanglement-assisted nonbinary quantum LDPC codes with finite field method

Jun-Hu, Shao; Zhou, Lin; Sun, Yu

doi:10.1109/iciea.2018.8397697

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…The F p m -linear CSS code is widely referred to as the CSS code in prior literature [10] [12]. We next discuss the structure and properties of the F p m -linear CSS code and the F p -linear CSS code over qudits in detail.…”

Section: Hd1mentioning

confidence: 99%

“…We note that the F p m -linear CSS codes over qudits have been proposed earlier in [10]. Other recent works on qudit CSS codes include [11], [12], [13], [14], and [15]. In [12], Shao et al use the F p m -linear CSS framework to construct the entanglement-assisted LDPC codes over qudits.…”

Section: Introductionmentioning

confidence: 99%

“…Other recent works on qudit CSS codes include [11], [12], [13], [14], and [15]. In [12], Shao et al use the F p m -linear CSS framework to construct the entanglement-assisted LDPC codes over qudits. While they provide the code parameters based on the F p m -linear CSS codes, the check matrix they provide is the check matrix of the F p -linear CSS code.…”

Section: Introductionmentioning

confidence: 99%

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$\mathbb {F}_p$-Linear and $\mathbb {F}_{p^m}$-Linear Qudit Codes From Dual-Containing Classical Codes

Nadkarni

Garani

2021

IEEE Trans. Quantum Eng.

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Quantum code construction from two classical codes D 1 [n, k 1 , d 1 ] and D 2 [n, k 2 , d 2 ] over the field F p m (p is prime and m is an integer) satisfying the dual containing criteria D ⊥ 1 ⊂ D 2 using the Calderbank-Shor-Steane (CSS) framework is well-studied. We show that the generalization of the CSS framework for qubits to qudits yields two different classes of codes, namely, the F p -linear CSS codes and the well-known F p m -linear CSS codes based on the check matrix-based definition and the coset-based definition of CSS codes over qubits Our contribution to this work are three-folds (a) We study the properties of the F p -linear and F p m -linear CSS codes and demonstrate the trade-off for designing codes with higher rates or better error detection and correction capability, useful for quantum systems. (b) For F p m -linear CSS codes, we provide the explicit form of the check matrix and show that the minimum distances d x and d z are equal to d 2 and d 1 , respectively, if and only if the code is non-degenerate. (c) We propose two classes of quantum codes obtained from the codes D 1 and D 2 , where one code is an F p l -linear code (l divides m) and the other code is obtained from a particular subgroup of the stabilizer group of the F p m -linear CSS code. Within each class of codes, we demonstrate the trade-off between higher rates and better error detection and correction capability. INDEX TERMSQuantum error correction, F p m -linear CSS codes, F p m -linear CSS codes, Dual containing codes, Qudit Codes, CSS-like codes.

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Section: Hd1mentioning

confidence: 99%