Related papers: Triorthogonal Codes and Self-dual Codes
A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors in 1997. At the same time we started studying first order difference ``black and white triangle operators (equations)'' on…
In two previous papers we have presented partition formulae for the Fibonacci numbers motivated by the appearance of the Fibonacci numbers in the representation theory of the 3-Kronecker quiver and its universal cover, the 3-regular tree.…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct…
Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…
We introduce the triangulant of two matrices, and relate it to the existence of orthogonal eigenvectors. We also use it for a new characterization of mutually unbiased bases. Generalizing the notion, we introduce higher order triangulants…
Decomposition of (finite-dimensional) operators in terms of orthogonal bases of matrices has been a standard method in quantum physics for decades. In recent years, it has become increasingly popular because of various methodologies applied…
As a candidate scheme for controllably coupled qubits, we consider two quantum dots, each doped with a single electron. The spin of the electron defines our qubit basis and trion states can be created by using polarized light; we show that…
We develop a connection between tripartite information $I_3$, secret sharing protocols and multi-unitaries. This leads to explicit ((2,3)) threshold schemes in arbitrary dimension minimizing tripartite information $I_3$. As an application…
This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…
We observe structure in the sequences of quotients and remainders of the Euclidean algorithm with two families of inputs. Analyzing the remainders, we obtain new algorithms for computing modular inverses and representating prime numbers by…
In this article, we introduce an algorithm for automatic generation and categorization of triangle geometry theorems.
Higher braiding gates, a new kind of quantum gate, are introduced. These are matrix solutions of the polyadic braid equations (which differ from the generalized Yang-Baxter equations). Such gates support a special kind of multi-qubit…
Discrete orthogonal matrices have several applications in information technology, such as in coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
This paper is on identification of classical information by the use of quantum channels. We focus on simultaneous ID codes which use measurements being useful to identify an arbitrary message. We give a direct and a converse part of the…
Orthogonal neural networks have recently been introduced as a new type of neural networks imposing orthogonality on the weight matrices. They could achieve higher accuracy and avoid evanescent or explosive gradients for deep architectures.…