Reginaldo Palazzo
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Reginaldo Palazzo has a total of 52 co-authors. Here are the top co-authors by number of shared publications:
- Antonio Aparecido de Andrade
Universidade Estadual Paulista "Julio de Mesquita Filho" - UNESP
8 shared publications - José Carmelo Interlando
Department of Mathematics and Statistics, San Diego State University, San Diego, USA
7 shared publications - Cibele Cristina Trinca
Department of Biotechnology and Bioprocess Engineering, Federal University of Tocantins, Gurupi, Brazil
5 shared publications - Clarice Dias de Albuquerque
Universidade Federal do Cariri (UFCA)
5 shared publications - Ricardo Augusto Watanabe
School of Mathematics, Statistics and Scientific Computing, Campinas State University, Campinas, Brazil
5 shared publications - Anderson José de Oliveira
Universidade Federal de Alfenas
3 shared publications
Latest Publications
- Open Access
Characterization of $n$-Dimensional Toric and Burst-Error-Correcting Quantum Codes from Lattice Codes
Quantum error correction is essential for the development of any scalable quantum computer. In this work we introduce a generalization of a quantum interleaving method for combating clusters of errors in toric quantum error-correcting codes. We present new $n$-dimensional toric quantum codes, where $n\geq 5$, which are featured by lattice codes and apply the proposed quantum interleaving method to such new $n$-dimensional toric quantum codes. Through the application of this method to these novel $n$-dimensional toric quantum codes we derive new $n$-dimensional quantum burst-error-correcting codes. Consequently, $n$-dimensional toric quantum codes and burst-error-correcting quantum codes are provided offering both a good code rate and a significant coding gain when it comes to toric quantum codes. Another important consequence from the presented $n$-dimensional toric quantum codes is that if the Golomb and Welch conjecture in \cite{perfcodes} regarding the Lee sphere in $n$ dimensions for the respective close packings holds true, then it follows that these $n$-dimensional toric quantum codes are the only possible ones to be obtained from lattice codes. Moreover, such a methodology can be applied for burst error correction in cases involving localized errors, quantum data storage and quantum channels with memory.Open AccessCharacterization of $n$-Dimensional Toric and Burst-Error-Correcting Quantum Codes from Lattice Codes
Quantum error correction is essential for the development of any scalable quantum computer. In this work we introduce a generalization of a quantum interleaving method for combating clusters of errors in toric quantum error-correcting codes. We present new $n$-dimensional toric quantum codes, where $n\geq 5$, which are featured by lattice codes and apply the proposed quantum interleaving method to such new $n$-dimensional toric quantum codes. Through the application of this method to these novel $n$-dimensional toric quantum codes we derive new $n$-dimensional quantum burst-error-correcting codes. Consequently, $n$-dimensional toric quantum codes and burst-error-correcting quantum codes are provided offering both a good code rate and a significant coding gain when it comes to toric quantum codes. Another important consequence from the presented $n$-dimensional toric quantum codes is that if the Golomb and Welch conjecture in \cite{perfcodes} regarding the Lee sphere in $n$ dimensions for the respective close packings holds true, then it follows that these $n$-dimensional toric quantum codes are the only possible ones to be obtained from lattice codes. Moreover, such a methodology can be applied for burst error correction in cases involving localized errors, quantum data storage and quantum channels with memory. - 21 April 2024
- Published by Springer Nature in Computational and Applied Mathematics
- Vol. 43 (4) , 1-24
On the properties of hyperelliptic functions and isometries for Fuchsian groups isomorphism in ${\mathbb {D}}^2$ and ${\mathbb {H}}^2$- 21 April 2024
- Published by Springer Nature in Computational and Applied Mathematics
- Vol. 43 (4) , 1-24
On the properties of hyperelliptic functions and isometries for Fuchsian groups isomorphism in ${\mathbb {D}}^2$ and ${\mathbb {H}}^2$- 25 January 2024
- Published by Springer Nature in Quantum Information Processing
- Vol. 23 (2) , 1-19
New three- and four-dimensional toric and burst error-correcting quantum codes
- 25 January 2024
- Published by Springer Nature in Quantum Information Processing
- Vol. 23 (2) , 1-19
New three- and four-dimensional toric and burst error-correcting quantum codes
- Open Access
New Three and Four-Dimensional Toric and Burst-Error-Correcting Quantum Codes
Ongoing research and experiments have enabled quantum memory to realize the storage of qubits. On the other hand, interleaving techniques are used to deal with burst of errors. Effective interleaving techniques for combating burst of errors by using classical error-correcting codes have been proposed in several articles found in the literature, however, to the best of our knowledge, little is known regarding interleaving techniques for combating clusters of errors in topological quantum error-correcting codes. Motivated by that, in this work, we present new three and four-dimensional toric quantum codes which are featured by lattice codes and apply a quantum interleaving method to such new three and four-dimensional toric quantum codes. By applying such a method to these new codes we provide new three and four-dimensional quantum burst-error-correcting codes. As a consequence, new three and four-dimensional toric and burst-error-correcting quantum codes are obtained which have better information rates than those three and four-dimensional toric quantum codes from the literature. In addition to these proposed three and four-dimensional quantum burst-error-correcting codes improve such information rates, they can be used for burst-error-correction in errors which are located, quantum data stored and quantum channels with memory.
Open AccessNew Three and Four-Dimensional Toric and Burst-Error-Correcting Quantum Codes
Ongoing research and experiments have enabled quantum memory to realize the storage of qubits. On the other hand, interleaving techniques are used to deal with burst of errors. Effective interleaving techniques for combating burst of errors by using classical error-correcting codes have been proposed in several articles found in the literature, however, to the best of our knowledge, little is known regarding interleaving techniques for combating clusters of errors in topological quantum error-correcting codes. Motivated by that, in this work, we present new three and four-dimensional toric quantum codes which are featured by lattice codes and apply a quantum interleaving method to such new three and four-dimensional toric quantum codes. By applying such a method to these new codes we provide new three and four-dimensional quantum burst-error-correcting codes. As a consequence, new three and four-dimensional toric and burst-error-correcting quantum codes are obtained which have better information rates than those three and four-dimensional toric quantum codes from the literature. In addition to these proposed three and four-dimensional quantum burst-error-correcting codes improve such information rates, they can be used for burst-error-correction in errors which are located, quantum data stored and quantum channels with memory.
- 12 May 2023
- Published by Springer Nature in Quantum Information Processing
- Vol. 22 (5) , 1-25
On the construction of new toric quantum codes and quantum burst-error-correcting codes
- 12 May 2023
- Published by Springer Nature in Quantum Information Processing
- Vol. 22 (5) , 1-25
On the construction of new toric quantum codes and quantum burst-error-correcting codes
- Open AccessAlgebraic and Geometric Characterizations Related to the Quantization Problem of the $C_{2,8}$ ChannelIn this paper, we consider the steps to be followed in the analysis and interpretation of the quantization problem related to the $C_{2,8}$ channel, where the Fuchsian differential equations, the generators of the Fuchsian groups, and the tessellations associated with the cases $g=2$ and $g=3$, related to the hyperbolic case, are determined. In order to obtain these results, it is necessary to determine the genus $g$ of each surface on which this channel may be embedded. After that, the procedure is to determine the algebraic structure (Fuchsian group generators) associated with the fundamental region of each surface. To achieve this goal, an associated linear second-order Fuchsian differential equation whose linearly independent solutions provide the generators of this Fuchsian group is devised. In addition, the tessellations associated with each analyzed case are identified. These structures are identified in four situations, divided into two cases $(g=2$ and $g=3)$, obtaining, therefore, both algebraic and geometric characterizations associated with quantizing the $C_{2,8}$ channel.Open AccessAlgebraic and Geometric Characterizations Related to the Quantization Problem of the $C_{2,8}$ ChannelIn this paper, we consider the steps to be followed in the analysis and interpretation of the quantization problem related to the $C_{2,8}$ channel, where the Fuchsian differential equations, the generators of the Fuchsian groups, and the tessellations associated with the cases $g=2$ and $g=3$, related to the hyperbolic case, are determined. In order to obtain these results, it is necessary to determine the genus $g$ of each surface on which this channel may be embedded. After that, the procedure is to determine the algebraic structure (Fuchsian group generators) associated with the fundamental region of each surface. To achieve this goal, an associated linear second-order Fuchsian differential equation whose linearly independent solutions provide the generators of this Fuchsian group is devised. In addition, the tessellations associated with each analyzed case are identified. These structures are identified in four situations, divided into two cases $(g=2$ and $g=3)$, obtaining, therefore, both algebraic and geometric characterizations associated with quantizing the $C_{2,8}$ channel.
- Open Access
On the Construction of New Toric Quantum Codes and Quantum Burst-Error Correcting Codes
A toric quantum error-correcting code construction procedure is presented in this work. A new class of an infinite family of toric quantum codes is provided by constructing a classical cyclic code on the square lattice $\mathbb{Z}_{q}\times \mathbb{Z}_{q}$ for all odd integers $q\geq 5$ and, consequently, new toric quantum codes are constructed on such square lattices regardless of whether $q$ can be represented as a sum of two squares. Furthermore this work supplies for each $q$ the polyomino shapes that tessellate the corresponding square lattices and, consequently, tile the lattice $\mathbb{Z}^{2}$. The channel without memory to be considered for these constructed toric quantum codes is symmetric, since the $\mathbb{Z}^{2}$-lattice is autodual. Moreover, we propose a quantum interleaving technique by using the constructed toric quantum codes which shows that the code rate and the coding gain of the interleaved toric quantum codes are better than the code rate and the coding gain of Kitaev's toric quantum codes for $q=2n+1$, where $n\geq 2$, and of an infinite class of Bombin and Martin-Delgado's toric quantum codes. In addition to the proposed quantum interleaving technique improves such parameters, it can be used for burst-error correction in errors which are located, quantum data stored and quantum channels with memory.Open AccessOn the Construction of New Toric Quantum Codes and Quantum Burst-Error Correcting Codes
A toric quantum error-correcting code construction procedure is presented in this work. A new class of an infinite family of toric quantum codes is provided by constructing a classical cyclic code on the square lattice $\mathbb{Z}_{q}\times \mathbb{Z}_{q}$ for all odd integers $q\geq 5$ and, consequently, new toric quantum codes are constructed on such square lattices regardless of whether $q$ can be represented as a sum of two squares. Furthermore this work supplies for each $q$ the polyomino shapes that tessellate the corresponding square lattices and, consequently, tile the lattice $\mathbb{Z}^{2}$. The channel without memory to be considered for these constructed toric quantum codes is symmetric, since the $\mathbb{Z}^{2}$-lattice is autodual. Moreover, we propose a quantum interleaving technique by using the constructed toric quantum codes which shows that the code rate and the coding gain of the interleaved toric quantum codes are better than the code rate and the coding gain of Kitaev's toric quantum codes for $q=2n+1$, where $n\geq 2$, and of an infinite class of Bombin and Martin-Delgado's toric quantum codes. In addition to the proposed quantum interleaving technique improves such parameters, it can be used for burst-error correction in errors which are located, quantum data stored and quantum channels with memory. - 8 April 2022
- Published by Springer Nature in Quantum Information Processing
- Vol. 21 (4) , 1-26
Euclidean and hyperbolic asymmetric topological quantum codes
- 8 April 2022
- Published by Springer Nature in Quantum Information Processing
- Vol. 21 (4) , 1-26
Euclidean and hyperbolic asymmetric topological quantum codes
- 4 May 2021
- Published by Springer Nature in Computational and Applied Mathematics
- Vol. 40 (4) , 1-25
Uniformization of hyperelliptic curves as a systematic approach to establishing decision regions of hyperbolic signal sets
- 4 May 2021
- Published by Springer Nature in Computational and Applied Mathematics
- Vol. 40 (4) , 1-25
Uniformization of hyperelliptic curves as a systematic approach to establishing decision regions of hyperbolic signal sets
- Open Access
- 1 January 2020
- Published by American Institute of Mathematical Sciences (AIMS) in Advances in Mathematics of Communications
- Vol. 14 (4) , 631-650
Abelian non-cyclic orbit codes and multishot subspace codes
In this paper we characterize the orbit codes as geometrically uniform codes. This characterization is based on the description of all isometries over a projective geometry. In addition, Abelian orbit codes are defined and a construction of Abelian non-cyclic orbit codes is presented. In order to analyze their structures, the concept of geometrically uniform partitions have to be reinterpreted. As a consequence, a substantial reduction in the number of computations needed to obtain the minimum subspace distance of these codes is achieved and established. An application of orbit codes to multishot subspace codes obtained according to a multi-level construction is provided.
- 1 January 2020
- Published by American Institute of Mathematical Sciences (AIMS) in Advances in Mathematics of Communications
- Vol. 14 (4) , 631-650
Open AccessAbelian non-cyclic orbit codes and multishot subspace codes
In this paper we characterize the orbit codes as geometrically uniform codes. This characterization is based on the description of all isometries over a projective geometry. In addition, Abelian orbit codes are defined and a construction of Abelian non-cyclic orbit codes is presented. In order to analyze their structures, the concept of geometrically uniform partitions have to be reinterpreted. As a consequence, a substantial reduction in the number of computations needed to obtain the minimum subspace distance of these codes is achieved and established. An application of orbit codes to multishot subspace codes obtained according to a multi-level construction is provided.