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

Journal of quantum computing

New Quantum Color Codes Based on Hyperbolic Geometry

Avaz Naghipour, Duc Manh Nguyen

Published Jan 1, 2022• 0 citations
Publisher

Abstract

In this paper, hyperbolic geometry is used to constructing new quantum color codes. We use hyperbolic tessellations and hyperbolic polygons to obtain them by pairing the edges on compact surfaces. These codes have minimum dis... | Find, read and cite all the research you need on Tech Science Press
DOI
10.32604/jqc.2022.033712

Related papers

Hyperbolic quantum color codes

Waldir Silva Soares, Eduardo Brandani da Silva

Current work presents a new approach to quantum color codes on compact surfaces with genus g\geq2 using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations. We show that this method may give rise to color codes with a very good parameters and we present tables with several examples of these codes whose parameters had not been shown before. We also present a family of codes with minimum distance d=4 and the encoding rate asymptotically going to 1 while n\rightarrow\infty.

Quantum Information and Computation•Mar 1, 2018•8 citations

Construction of New Quantum Color Codes

This paper presents a hyperbolic geometry approach to the construction of new quantum color codes.The families of quantum color codes are constructed based on the identification of compact surfaces by hyperbolic tessellations.Codes of these families have 4 and 6 minimum distances and their encoding rate are near to 1.We also provide some quantum color codes with minimum distance of at least eight and a comparison table of quantum codes.

Quantum Physics Letters•Dec 1, 2022•0 citations

Hyperbolic quantum color codes

Eduardo Brandani da Silva, Waldir Silva Soares

Current work presents a new approach to quantum color codes on compact surfaces with genus $g \geq 2$ using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations. We show that this method may give rise to color codes with a very good parameters and we present tables with several examples of these codes whose parameters had not been shown before. We also present a family of codes with minimum distance $d=4$ and the encoding rate asymptotically going to 1 while $n \rightarrow \infty$.

arXiv:1804.06382•Apr 17, 2018•1 citation

Floquet Codes from Derived Semi-Regular Hyperbolic Tessellations on Orientable and Non-Orientable Surfaces

Douglas F. Copatti, Giuliano G. La Guardia, Waldir S. Soares +2 more

In this paper, we construct several new quantum Floquet codes on compact, orientable, as well as non-orientable surfaces. In order to obtain such codes, we identify these surfaces with hyperbolic polygons and examine hyperbolic semi-regular tessellations on such surfaces. The method of construction presented here generalizes similar constructions concerning hyperbolic Floquet codes on connected and compact surfaces with genus $g \geq 2$. A performance analysis and an investigation of the asymptotic behavior of these codes are also presented.

quant-pharXiv:2603.29811•Apr 1, 2026•0 citations

Construction of new quantum color codes

Avaz Naghipour, Duc Manh Nguyen

Abstract This paper presents a hyperbolic geometry approach to the construction of new quantum color codes. The families of quantum color codes are constructed based on the identification of compact surfaces by hyperbolic tessellations. Codes of these families have 4 and 6 minimum distances and their encoding rate are near to 1. We also provide some quantum color codes with minimum distance of at least eight and a comparison table of quantum codes.

•May 17, 2022•0 citations

Construction of Polygonal Color Codes from Hyperbolic Tesselations

W.S. SOARES JR, E.B. SILVA, E.J. VIZENTIM +1 more

ABSTRACT This current work propose a technique to generate polygonal color codes in the hyperbolic geometry environment. The color codes were introduced by Bombin and Martin-Delgado in 2007, and the called triangular color codes have a higher degree of interest because they allow the implementation of the Clifford group, but they encode only one qubit. In 2018 Soares e Silva extended the triangular codes to the polygonal codes, which encode more qubits. Using an approach through hyperbolic tessellations we show that it is possible to generate Hyperbolic Polygonal codes, which encode more than one qubit with the capacity to implement the entire Clifford group and also having a better coding rate than the previously mentioned codes, for the color codes on surfaces with boundary with minimum distance d = 3.

•Apr 1, 2020•0 citations
Current work presents a new approach to quantum color codes on compact surfaces with genus g\geq2 using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations. We show that this method may give rise to color codes with a very good parameters and we present tables with several examples of these codes whose parameters had not been shown before. We also present a family of codes with minimum distance d=4 and the encoding rate asymptotically going to 1 while n\rightarrow\infty.
Current work presents a new approach to quantum color codes on compact surfaces with genus g≥2g \geq 2g≥2 using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations. We show that this method may give rise to color codes with a very good parameters and we present tables with several examples of these codes whose parameters had not been shown before. We also present a family of codes with minimum distance d=4d=4d=4 and the encoding rate asymptotically going to 1 while n→∞n \rightarrow \inftyn→∞.
In this paper, we construct several new quantum Floquet codes on compact, orientable, as well as non-orientable surfaces. In order to obtain such codes, we identify these surfaces with hyperbolic polygons and examine hyperbolic semi-regular tessellations on such surfaces. The method of construction presented here generalizes similar constructions concerning hyperbolic Floquet codes on connected and compact surfaces with genus g≥2g \geq 2g≥2. A performance analysis and an investigation of the asymptotic behavior of these codes are also presented.
ABSTRACT This current work propose a technique to generate polygonal color codes in the hyperbolic geometry environment. The color codes were introduced by Bombin and Martin-Delgado in 2007, and the called triangular color codes have a higher degree of interest because they allow the implementation of the Clifford group, but they encode only one qubit. In 2018 Soares e Silva extended the triangular codes to the polygonal codes, which encode more qubits. Using an approach through hyperbolic tessellations we show that it is possible to generate Hyperbolic Polygonal codes, which encode more than one qubit with the capacity to implement the entire Clifford group and also having a better coding rate than the previously mentioned codes, for the color codes on surfaces with boundary with minimum distance d = 3.