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

TEMA (São Carlos)

Construction of Polygonal Color Codes from Hyperbolic Tesselations

Waldir Silva Soares, Eduardo Brandani da Silva, E.J. VIZENTIM, Franciele P. B. Soares

Published Mar 27, 2020• 0 citations
Publisher

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.

DOI
10.5540/tema.2020.021.01.43

Related papers

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

Construction of color codes from polygons

Eduardo Brandani da Silva, Waldir Silva Soares

We propose a procedure for constructing new classes of codes, called polygonal color codes. This technique expands the triangular color codes introduced by Bombin and Martin-Delgado in 2007. Triangular color codes, built on a two-dimensional Euclidean surface with three edges, implement the entire Clifford group, but they only encode one qubit. In our case, polygonal color codes are constructed on two-dimensional surfaces with n edges, with n ≥ 3 , increasing the number of encoded qubits. Considering a surface with boundary and evaluating the generators of the first homology group of this surface, we may increase the dimension of the code without losing the transversal implementation of the Clifford group. In addition, we construct two codes, one with 2 and one with 3 encoded qubits, which exemplify the method and show that we can generate codes with better parameters than the known triangular codes. For one of these constructions, we also give general parameters.

Journal of Physics Communications•Jul 2, 2018•4 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

Hyperbolic color codes with constant rate and polynomial distance

Shun Hasegawa, Hayata Yamasaki

Recent advances in quantum hardware relax the strict geometric-locality constraints traditionally imposed on quantum error-correcting codes, motivating interest in high-rate quantum low-density parity-check (qLDPC) codes. At the same time, color codes provide a particularly rich setting for fault-tolerant quantum computation, underlying protocols such as single-shot error correction and self-correcting quantum computation. Hyperbolic color codes provide a class of high-rate qLDPC codes that also retain the structural features of color codes relevant to fault-tolerant quantum computation. However, previous constructions of hyperbolic color codes have achieved at most logarithmic code distance. In this work, we construct hyperbolic color codes with both constant rate and polynomial distance by building on arithmetic hyperbolic manifolds that support polynomial-distance hyperbolic toric codes. Our construction applies in arbitrary dimension \(D\geq 4\). In even dimensions, the resulting type-\(D/2\) color codes have constant encoding rate and polynomial distance, while in other cases the number of logical qubits and the code distance both exhibit polynomial scaling. We further derive explicit exponents for polynomial lower bounds as functions of the dimension and code type. These results establish a family of hyperbolic color codes simultaneously achieving constant rate and polynomial distance and providing a testbed to explore fault-tolerant quantum computation protocols that combine high-rate quantum codes with the structural advantages of color codes.

quant-pharXiv:2609.16125•Sep 16, 2026•0 citations

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

New Quantum Color Codes Based on Hyperbolic Geometry

Avaz Naghipour, Duc Manh Nguyen

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

Journal of quantum computing•Jan 1, 2022•0 citations
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.
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.
We propose a procedure for constructing new classes of codes, called polygonal color codes. This technique expands the triangular color codes introduced by Bombin and Martin-Delgado in 2007. Triangular color codes, built on a two-dimensional Euclidean surface with three edges, implement the entire Clifford group, but they only encode one qubit. In our case, polygonal color codes are constructed on two-dimensional surfaces with n edges, with n ≥ 3 , increasing the number of encoded qubits. Considering a surface with boundary and evaluating the generators of the first homology group of this surface, we may increase the dimension of the code without losing the transversal implementation of the Clifford group. In addition, we construct two codes, one with 2 and one with 3 encoded qubits, which exemplify the method and show that we can generate codes with better parameters than the known triangular codes. For one of these constructions, we also give general parameters.
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→∞.
Recent advances in quantum hardware relax the strict geometric-locality constraints traditionally imposed on quantum error-correcting codes, motivating interest in high-rate quantum low-density parity-check (qLDPC) codes. At the same time, color codes provide a particularly rich setting for fault-tolerant quantum computation, underlying protocols such as single-shot error correction and self-correcting quantum computation. Hyperbolic color codes provide a class of high-rate qLDPC codes that also retain the structural features of color codes relevant to fault-tolerant quantum computation. However, previous constructions of hyperbolic color codes have achieved at most logarithmic code distance. In this work, we construct hyperbolic color codes with both constant rate and polynomial distance by building on arithmetic hyperbolic manifolds that support polynomial-distance hyperbolic toric codes. Our construction applies in arbitrary dimension D≥4D\geq 4D≥4. In even dimensions, the resulting type-D/2D/2D/2 color codes have constant encoding rate and polynomial distance, while in other cases the number of logical qubits and the code distance both exhibit polynomial scaling. We further derive explicit exponents for polynomial lower bounds as functions of the dimension and code type. These results establish a family of hyperbolic color codes simultaneously achieving constant rate and polynomial distance and providing a testbed to explore fault-tolerant quantum computation protocols that combine high-rate quantum codes with the structural advantages of color codes.
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.