Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2105.01144 · Quantum Information Processing

Euclidean and hyperbolic asymmetric topological quantum codes

Clarice Dias de Albuquerque, Giuliano G. La Guardia, Reginaldo Palazzo, Cátia Regina de Oliveira Quilles Queiroz, Vandenberg Lopes Vieira

Published Apr 1, 2022• 7 citations
arXivHTMLPDF
DOI
10.1007/s11128-022-03488-8

Related papers

$ t_1 $ -partitioned Euclidean orthogonal MP codes and their application to asymmetric quantum codes

Ye Cai Guo, Peng Hu, Xiusheng Liu

In this paper, we first give the definition of $ t_1 $-partitioned Euclidean orthogonal matrix-product (MP) codes over finite fields. We then provide a criterion for $ t_1 $-partitioned Euclidean orthogonal MP codes over finite fields to be Euclidean dual-containing. Further, we exhibit a new construction method for asymmetric quantum codes by using this criterion. This construction is applied to obtain six new infinite families of asymmetric quantum codes. In addition, we compare our asymmetric quantum codes with previously known asymmetric quantum codes or quantum codes available in the literature. As can be seen, our obtained asymmetric quantum codes have better parameters than the asymmetric quantum codes or quantum codes available in the literature.

Advances in Mathematics of Communications•Aug 18, 2025•0 citations

Topological Quantum Codes

Clarice Dias de Albuquerque, Eduardo Brandani da Silva, Waldir Silva Soares

SpringerBriefs in mathematics•Jan 1, 2022•0 citations

Optimal Asymmetric Quantum Codes from the Euclidean Sums of Linear Codes

Peng Xu, Xiusheng Liu

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.

Wuhan University Journal of Natural Sciences•Feb 1, 2024•0 citations

Quantum Codes for Topological Quantum Computation

Clarice Dias de Albuquerque, Eduardo Brandani da Silva, Waldir Silva Soares

SpringerBriefs in mathematics•Jan 1, 2022•3 citations

Hyperbolic Topological Quantum Sources

Lu He, Lei Huang, Weixuan Zhang +8 more

Robust Integrable Quantum Optical Sources, Constructed by Topological Boundary States, Are Crucial for the on-chip Quantum Information Processing. However, Limited by the Bulk-edge Correspondence, the Implementation of Topological Boundary Channels Necessitates a Substantial Number of Bulk Sites, Which Notably Diminishes the Ratio of Ring Resonators to Generate Quantum Sources. How to Achieve Topologically-protected Quantum Sources With the Extremely Enhanced Utilization Efficiency of Optical Resonators Remains a Challenge. Here, the First Realization of Hyperbolic Topological Quantum Sources is reported, Which Possess a Dominated Number of Boundary Resonators Than That in the Bulk Domain. Specifically, Hyperbolic Topological Quantum Sources Require Fewer Resources (i.e., the number of ring resonators) to Achieve the Same Level of Brightness Compared With Euclidean Topological Quantum Sources. Furthermore, the Robust Correlated- and Entangled-photon Pairs Are Measured. The Work Possesses Potential Applications in Integrable Quantum Circuits and Suggests a Novel Way on the Exploration of Quantum Physics in Non-Euclidean Space.

Advanced Science•Mar 17, 2025•3 citations

Quantum Computation with Topological Codes

Keisuke Fujii

SpringerBriefs in mathematical physics•Jan 1, 2015•59 citations
In this paper, we first give the definition of $ t_1 $-partitioned Euclidean orthogonal matrix-product (MP) codes over finite fields. We then provide a criterion for $ t_1 $-partitioned Euclidean orthogonal MP codes over finite fields to be Euclidean dual-containing. Further, we exhibit a new construction method for asymmetric quantum codes by using this criterion. This construction is applied to obtain six new infinite families of asymmetric quantum codes. In addition, we compare our asymmetric quantum codes with previously known asymmetric quantum codes or quantum codes available in the literature. As can be seen, our obtained asymmetric quantum codes have better parameters than the asymmetric quantum codes or quantum codes available in the literature.
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.
Robust Integrable Quantum Optical Sources, Constructed by Topological Boundary States, Are Crucial for the on-chip Quantum Information Processing. However, Limited by the Bulk-edge Correspondence, the Implementation of Topological Boundary Channels Necessitates a Substantial Number of Bulk Sites, Which Notably Diminishes the Ratio of Ring Resonators to Generate Quantum Sources. How to Achieve Topologically-protected Quantum Sources With the Extremely Enhanced Utilization Efficiency of Optical Resonators Remains a Challenge. Here, the First Realization of Hyperbolic Topological Quantum Sources is reported, Which Possess a Dominated Number of Boundary Resonators Than That in the Bulk Domain. Specifically, Hyperbolic Topological Quantum Sources Require Fewer Resources (i.e., the number of ring resonators) to Achieve the Same Level of Brightness Compared With Euclidean Topological Quantum Sources. Furthermore, the Robust Correlated- and Entangled-photon Pairs Are Measured. The Work Possesses Potential Applications in Integrable Quantum Circuits and Suggests a Novel Way on the Exploration of Quantum Physics in Non-Euclidean Space.