We craft a special class of unitary matrices over $\mathbb{F}q^{2}$ to generate classical linear codes whose Hermitian hulls have dimensions that we can design. We then use the codes as classical ingredients in the construction of good entanglement-assisted quantum codes. Over finite fields of characteristic 2, we propose two explicit constructions. To highlight their efficacy, we list excellent qubit codes whose parameters are either new or strictly better than comparable best-known codes in the literature.We craft a special class of unitary matrices over$\mathbb{F}q^{2}$to generate classical linear codes whose Hermitian hulls have dimensions that we can design. We then use the codes as classical ingredients in the construction of good entanglement-assisted quantum codes. Over finite fields of characteristic 2, we propose two explicit constructions. To highlight their efficacy, we list excellent qubit codes whose parameters are either new or strictly better than comparable best-known codes in the literature.

IEEE International Symposium on Information Theory (ISIT)Jul 7, 20243 citations

Entanglement-assisted quantum codes from matrix-product codes

Xiusheng Liu, Hualu Liu, Long Yu

Quantum Information ProcessingMay 4, 201933 citations

Entanglement-assisted quantum codes from arbitrary binary linear codes

Jianfa Qian, Lina Zhang

Designs Codes and CryptographyJul 25, 201454 citations

Minimal-Entanglement Entanglement-Assisted Quantum Error Correction Codes from Modified Circulant Matrices

Duc Manh Nguyen, Sunghwan Kim

In this paper, new construction methods of entanglement-assisted quantum error correction code (EAQECC) from circulant matrices are proposed. We first construct the matrices from two vectors of constraint size, and determine the isotropic subgroup. Then, we also propose a method for calculation of the entanglement subgroup based on standard forms of binary matrices to satisfy the constraint conditions of EAQECC. With isotropic and entanglement subgroups, we determine all the parameters and the minimum distance of the EAQECC. The proposed EAQECC with small lengths are presented to explain the practicality of this construction of EAQECC. Comparison with some earlier constructions of EAQECC shows that the proposed EAQECC is better.In this paper, new construction methods of entanglement-assisted quantum error correction code (EAQECC) from circulant matrices are proposed. We first construct the matrices from two vectors of constraint size, and determine the isotropic subgroup. Then, we also propose a method for calculation of the entanglement subgroup based on standard forms of binary matrices to satisfy the constraint conditions of EAQECC. With isotropic and entanglement subgroups, we determine all the parameters and the minimum distance of the EAQECC. The proposed EAQECC with small lengths are presented to explain the practicality of this construction of EAQECC. Comparison with some earlier constructions of EAQECC shows that the proposed EAQECC is better.

SymmetryJul 18, 201715 citations

Entanglement assisted quantum error correcting code from Hadamard matrices

Min Liu, Xiaoqing Tan, Daipengwei Bao +1 more

The classical linear codes that construct quantum error correction codes need to meet certain specific conditions. The proposal of entanglement-assisted quantum error correcting codes eliminates the restriction of these conditions, so all classical linear codes can be constructed into entanglement-assisted quantum error correcting codes. The Hadamard matrix is a special type of orthogonal matrix. Hadamard codes, constructed based on the standard form of Hadamard matrices, are a type of linear complementary dual (LCD) codes. By extending the generator and parity-check matrices of Hadamard codes, two types of classical codes whose parameters are [(l+1)(n−1), n−1] and [3n−3, n−1] maintain the LCD property. Utilizing the relationship between their LCD property and the dimensions of the Euclidean hull, this paper constructs two types of EAQECCs based on Hadamard matrices. These EAQECCs can achieve maximal entanglement, resulting in higher code rates and net rates compared to other EAQECCs. Their parameters are [[3n−3, 2n−2, d≥1; n−1]] and [[2n−2, n−1, d≥1; n−1]], respectively.The classical linear codes that construct quantum error correction codes need to meet certain specific conditions. The proposal of entanglement-assisted quantum error correcting codes eliminates the restriction of these conditions, so all classical linear codes can be constructed into entanglement-assisted quantum error correcting codes. The Hadamard matrix is a special type of orthogonal matrix. Hadamard codes, constructed based on the standard form of Hadamard matrices, are a type of linear complementary dual (LCD) codes. By extending the generator and parity-check matrices of Hadamard codes, two types of classical codes whose parameters are [(l+1)(n−1), n−1] and [3n−3, n−1] maintain the LCD property. Utilizing the relationship between their LCD property and the dimensions of the Euclidean hull, this paper constructs two types of EAQECCs based on Hadamard matrices. These EAQECCs can achieve maximal entanglement, resulting in higher code rates and net rates compared to other EAQECCs. Their parameters are [[3n−3, 2n−2, d≥1; n−1]] and [[2n−2, n−1, d≥1; n−1]], respectively.

Zhongguo kexue. Wulixue Lixue TianwenxueSep 19, 20240 citations

New constructions of entanglement-assisted quantum codes

Adel N. Alahmadi, Ahmad N. Al‐Kenani, Rola Hijazi +3 more

Cryptography and CommunicationsJun 26, 202125 citations

We craft a special class of unitary matrices over

\mathbb{F}q^{2}

to generate classical linear codes whose Hermitian hulls have dimensions that we can design. We then use the codes as classical ingredients in the construction of good entanglement-assisted quantum codes. Over finite fields of characteristic 2, we propose two explicit constructions. To highlight their efficacy, we list excellent qubit codes whose parameters are either new or strictly better than comparable best-known codes in the literature.