Quantum Information Processing

Maximal entanglement-assisted quantum error correction codes from the skew group ring $${\mathbb {F}}_4 \rtimes _{\varphi } G$$ by a heuristic search scheme

Serap Şahinkaya, Adrian Korban, Deniz Üstün

Published Apr 1, 2022• 8 citations

Publisher

DOI: 10.1007/s11128-022-03500-1

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Abstract In this paper, we explore the algebraic structure of skew-G codes over the ring $$A= \mathbb {F}_4[u,v]/\langle u^2, v^2, uv - vu \rangle $$ A = F 4 [ u , v ] / ⟨ u 2 , v 2 , u v - v u ⟩ . In addition to that, we bridge theoretical results with practical applications in quantum computing. More specifically, we derive a significant number of new binary EAQEC codes from the gray images of the skew-G codes over A according to Grassl’s codetable [14].

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Quantum Information Processing

Maximal entanglement-assisted quantum error correction codes from the skew group ring ${\mathbb {F}}_4 \rtimes _{\varphi } G$ by a heuristic search schemeMaximal entanglement-assisted quantum error correction codes from the skew group ring $${\mathbb {F}}_4 \rtimes _{\varphi } G$$ by a heuristic search scheme

Serap Şahinkaya, Adrian Korban, Deniz Üstün

Published Apr 1, 2022• 8 citations

Publisher

DOI: 10.1007/s11128-022-03500-1

Related papers

Entanglement-Assisted Quantum Error-Correcting Codes

Todd A. Brun, Min-Hsiu Hsieh

We provide a self-contained introduction for entanglement-assisted quantum error-correcting codes in this book chapter.

arXiv:1610.04013Oct 13, 20160 citations

Entanglement-assisted binary quantum codes from skew cyclic codes over ${\mathbb {F}}_2 \times ({\mathbb {F}}_2+v{\mathbb {F}}_2)$ Entanglement-assisted binary quantum codes from skew cyclic codes over $${\mathbb {F}}_2 \times ({\mathbb {F}}_2+v{\mathbb {F}}_2)$$

Fatma Çalışkan, Refia Aksoy, Nuh Aydın +1 more

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Skew G-codes over $\mathbb {F}_4[u,v]/\langle u^2, v^2, uv-vu \rangle$ and new binary entanglement-assisted quantum error-correcting codesSkew G-codes over $$\mathbb {F}_4[u,v]/\langle u^2, v^2, uv-vu \rangle $$ and new binary entanglement-assisted quantum error-correcting codes

Serap Şahinkaya, Deniz Üstün

Abstract In this paper, we explore the algebraic structure of skew-G codes over the ring $A= \mathbb {F}_4[u,v]/\langle u^2, v^2, uv - vu \rangle$ A = F 4 [ u , v ] / ⟨ u 2 , v 2 , u v - v u ⟩ . In addition to that, we bridge theoretical results with practical applications in quantum computing. More specifically, we derive a significant number of new binary EAQEC codes from the gray images of the skew-G codes over A according to Grassl’s codetable [14].Abstract In this paper, we explore the algebraic structure of skew-G codes over the ring $$A= \mathbb {F}_4[u,v]/\langle u^2, v^2, uv - vu \rangle $$ A = F 4 [ u , v ] / ⟨ u 2 , v 2 , u v - v u ⟩ . In addition to that, we bridge theoretical results with practical applications in quantum computing. More specifically, we derive a significant number of new binary EAQEC codes from the gray images of the skew-G codes over A according to Grassl’s codetable [14].

Quantum Information ProcessingJun 27, 20251 citation

Entanglement-assisted quantum codes from Galois LCD codes

Xiusheng Liu, Hualu Liu, Long Yu

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard quantum error-correcting codes, which can only be constructed from dual-containing codes. However, the parameter of ebits $c$ is usually calculated by computer search. In this paper, we construct four classes of MDS entanglement-assisted quantum error-correcting codes (MDS EAQECCs) based on $k$ -Galois LCD MDS codes for some certain code lengths, where the parameter of ebits $c$ can be easily generated algebraically and not by computational search. Moreover, the constructed four classes of EAQECCs are also maximal-entanglement EAQECCs.Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard quantum error-correcting codes, which can only be constructed from dual-containing codes. However, the parameter of ebits $c$ is usually calculated by computer search. In this paper, we construct four classes of MDS entanglement-assisted quantum error-correcting codes (MDS EAQECCs) based on $k$-Galois LCD MDS codes for some certain code lengths, where the parameter of ebits $c$ can be easily generated algebraically and not by computational search. Moreover, the constructed four classes of EAQECCs are also maximal-entanglement EAQECCs.

arXiv:1809.00568Sep 3, 20187 citations

Constructions of good entanglement-assisted quantum error correcting codes

Kenza Guenda, Somphong Jitman, Thomas Aaron Gulliver

arXiv:1606.00134Designs Codes and CryptographyJan 25, 2017256 citations

A new method for constructing EAQEC MDS codes

Peng Hu, Xiusheng Liu

Entanglement-assisted quantum error-correcting (EAQEC) codes make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQEC code from any classical linear code, unlike standard quantum error-correcting codes, which can only be constructed from dual-containing codes. However, the number $c$ of pre-shared maximally entangled states is usually calculated by computer search. In this paper, we first give a new formula for calculating the number $c$ of pre-shared maximally entangled states. Then, using this formula, we construct three classes of new entanglement-assisted quantum error-correcting maximum-distance-separable ( EAQEC MDS) codes.Entanglement-assisted quantum error-correcting (EAQEC) codes make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQEC code from any classical linear code, unlike standard quantum error-correcting codes, which can only be constructed from dual-containing codes. However, the number $c$ of pre-shared maximally entangled states is usually calculated by computer search. In this paper, we first give a new formula for calculating the number $c$ of pre-shared maximally entangled states. Then, using this formula, we construct three classes of new entanglement-assisted quantum error-correcting maximum-distance-separable ( EAQEC MDS) codes.

arXiv:2003.00843Mar 2, 20202 citations

Maximal entanglement-assisted quantum error correction codes from the skew group ring

{\mathbb {F}}_4 \rtimes _{\varphi } G

by a heuristic search scheme

Entanglement-assisted binary quantum codes from skew cyclic codes over

{\mathbb {F}}_2 \times ({\mathbb {F}}_2+v{\mathbb {F}}_2)

Skew G-codes over

\mathbb {F}_4[u,v]/\langle u^2, v^2, uv-vu \rangle

and new binary entanglement-assisted quantum error-correcting codes

Abstract In this paper, we explore the algebraic structure of skew-G codes over the ring

A= \mathbb {F}_4[u,v]/\langle u^2, v^2, uv - vu \rangle

A = F 4 [ u , v ] / ⟨ u 2 , v 2 , u v - v u ⟩ . In addition to that, we bridge theoretical results with practical applications in quantum computing. More specifically, we derive a significant number of new binary EAQEC codes from the gray images of the skew-G codes over A according to Grassl’s codetable [14].

c

is usually calculated by computer search. In this paper, we construct four classes of MDS entanglement-assisted quantum error-correcting codes (MDS EAQECCs) based on

k

-Galois LCD MDS codes for some certain code lengths, where the parameter of ebits

c

can be easily generated algebraically and not by computational search. Moreover, the constructed four classes of EAQECCs are also maximal-entanglement EAQECCs.

c

of pre-shared maximally entangled states is usually calculated by computer search. In this paper, we first give a new formula for calculating the number

c

of pre-shared maximally entangled states. Then, using this formula, we construct three classes of new entanglement-assisted quantum error-correcting maximum-distance-separable ( EAQEC MDS) codes.