Asymmetric entanglement-assisted quantum error-correcting MDS codes of physical qubits $p^{s}$ over $\mathbb{F}_{p^{m}}$ Asymmetric entanglement-assisted quantum error-correcting MDS codes of physical qubits $p^{s}$ over $\mathbb{F}_{p^{m}}$

Hai Quang Dinh, Bac Trong Nguyen, Hiep L. Thi +2 more

In this paper, we construct entanglement-assisted quantum error-correcting codes (EAQEC codes) of physical qubits $p^{s}$ over $\mathbb{F}_{p^{m}}$ . We compare our EAQEC codes with all known EAQEC codes to see that our EAQEC codes are new in the sense that their parameters are different from all the previous constructions. If we fix the physical qubits and the logical qubits of EAQEC codes, many of them have larger quantum distances than the well known EAQEC codes in the literature. Moreover, some of our EAQEC codes achieve larger quantum distances while requiring fewer or the same number of entangled bits compared with existing EAQEC codes when the numbers of physical qubits and logical qubits are fixed. We construct asymmetric entanglement-assisted quantum error-correcting (AEAQEC) MDS codes of physical qubits $p^{s}$ over $\mathbb{F}_{p^{m}}$ . When the physical qubits of the AEAQEC codes is fixed, many of our AEAQEC codes have a significantly larger number of quantum distances compared to all previously constructed AEAQEC codes. We also provide a version of Singleton bound for all AEAQEC codes.In this paper, we construct entanglement-assisted quantum error-correcting codes (EAQEC codes) of physical qubits $p^{s}$ over $\mathbb{F}_{p^{m}}$ . We compare our EAQEC codes with all known EAQEC codes to see that our EAQEC codes are new in the sense that their parameters are different from all the previous constructions. If we fix the physical qubits and the logical qubits of EAQEC codes, many of them have larger quantum distances than the well known EAQEC codes in the literature. Moreover, some of our EAQEC codes achieve larger quantum distances while requiring fewer or the same number of entangled bits compared with existing EAQEC codes when the numbers of physical qubits and logical qubits are fixed. We construct asymmetric entanglement-assisted quantum error-correcting (AEAQEC) MDS codes of physical qubits $p^{s}$ over $\mathbb{F}_{p^{m}}$ . When the physical qubits of the AEAQEC codes is fixed, many of our AEAQEC codes have a significantly larger number of quantum distances compared to all previously constructed AEAQEC codes. We also provide a version of Singleton bound for all AEAQEC codes.

EPJ Quantum TechnologyJun 17, 20260 citations

l-LCP of codes and their applications to EAQEC codes

Jie Liu, Xiusheng Liu

Quantum Information ProcessingApr 28, 202313 citations

Entanglement-assisted quantum error-correcting codes and asymmetric entanglement-assisted quantum error-correcting codes of length 5pt over 𝔽pm

Hai Quang Dinh, Bac Trong Nguyen, Van‐Nui Nguyen +1 more

Classical cyclic and constacyclic codes play a fundamental role in coding theory, thanks to their rich algebraic structures and efficient encoding/decoding algorithms. These codes are especially important in the construction of quantum error-correcting codes, since their inherent algebraic properties facilitate the derivation of self-orthogonality or dual-containing conditions that are crucial for ensuring quantum error correction capability. In this paper, we construct entanglement-assisted quantum error-correcting codes (EAQEC codes) of length [Formula: see text] over [Formula: see text]. We compare our EAQEC codes with all known EAQEC codes to see that our EAQEC codes are new in the sense that their parameters are different from all the previous constructions. Moreover, our EAQEC codes have shorter lengths than the known codes, yet exhibit significantly larger quantum distances. This is highly meaningful in the context of quantum error correction, as it enables the construction of codes with small lengths while maintaining large quantum distances. We also construct asymmetric EAQEC (AEAQEC) codes of length [Formula: see text] over [Formula: see text]. We evaluate our AEAQEC codes against all existing ones and find that they are both new and better.Classical cyclic and constacyclic codes play a fundamental role in coding theory, thanks to their rich algebraic structures and efficient encoding/decoding algorithms. These codes are especially important in the construction of quantum error-correcting codes, since their inherent algebraic properties facilitate the derivation of self-orthogonality or dual-containing conditions that are crucial for ensuring quantum error correction capability. In this paper, we construct entanglement-assisted quantum error-correcting codes (EAQEC codes) of length [Formula: see text] over [Formula: see text]. We compare our EAQEC codes with all known EAQEC codes to see that our EAQEC codes are new in the sense that their parameters are different from all the previous constructions. Moreover, our EAQEC codes have shorter lengths than the known codes, yet exhibit significantly larger quantum distances. This is highly meaningful in the context of quantum error correction, as it enables the construction of codes with small lengths while maintaining large quantum distances. We also construct asymmetric EAQEC (AEAQEC) codes of length [Formula: see text] over [Formula: see text]. We evaluate our AEAQEC codes against all existing ones and find that they are both new and better.

International Journal of Modern Physics CFeb 27, 20260 citations

A Unification of the Coding Theory and OAQEC Perspectives on Hybrid Codes

Shayan Majidy

arXiv:1806.03702International Journal of Theoretical PhysicsAug 7, 20237 citations

Asymmetric entanglement-assisted quantum error-correcting MDS codes of physical qubits

p^{s}

over

\mathbb{F}_{p^{m}}

In this paper, we construct entanglement-assisted quantum error-correcting codes (EAQEC codes) of physical qubits

p^{s}

over

\mathbb{F}_{p^{m}}

. We compare our EAQEC codes with all known EAQEC codes to see that our EAQEC codes are new in the sense that their parameters are different from all the previous constructions. If we fix the physical qubits and the logical qubits of EAQEC codes, many of them have larger quantum distances than the well known EAQEC codes in the literature. Moreover, some of our EAQEC codes achieve larger quantum distances while requiring fewer or the same number of entangled bits compared with existing EAQEC codes when the numbers of physical qubits and logical qubits are fixed. We construct asymmetric entanglement-assisted quantum error-correcting (AEAQEC) MDS codes of physical qubits

p^{s}

over

\mathbb{F}_{p^{m}}

. When the physical qubits of the AEAQEC codes is fixed, many of our AEAQEC codes have a significantly larger number of quantum distances compared to all previously constructed AEAQEC codes. We also provide a version of Singleton bound for all AEAQEC codes.