Related papers: The bitwise operations in relation to obtaining La…
In this paper we give complete descriptions of the set of square roots of certain classical operators, often providing specific formulas. The classical operators included in this discussion are the square of the unilateral shift, the…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
A Latin square $L(n,k)$ is a square of order $n$ with its entries colored with $k$ colors so that all the entries in a row or column have different colors. Let $d(L(n,k))$ be the minimal number of colored entries of an $n \times n$ square…
This paper suggests integrating one-dimensional optimization methods to tackle diverse problems, emphasizing their significance in resolving practical issues and applying mathematical principles to real-world contexts. It focuses on…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
The logarithm of the maximum number of transversals over all latin squares of order $n$ is greater than $\frac{n}{6}(\ln n+ O(1))$.
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
The bit-reversed permutation is a famous task in signal processing and is key to efficient implementation of the fast Fourier transform. This paper presents optimized C++11 implementations of five extant methods for computing the…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
A study of the existing linear algebra libraries that you can use from C++
This is a translation of Leonhard Euler's ``De quadratis magicis'' . It is E795 in the Enestrom index. This paper studies how to construct magic squares with certain numbers of cells, in particular 9, 16, 25 and 36. It considers some…
Latin squares have been historically used in order to create statistical designs in which, starting from a small number of experiments, it can be obtained a large experimental space. In this sense, the optimization of the selection of Latin…
Difference arrays are used in applications such as software testing, authentication codes and data compression. Pseudo-orthogonal Latin squares are used in experimental designs. A special class of pseudo-orthogonal Latin squares are the…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
A latin square of order $n$ with pairwise disjoint subsquares of orders $h_1,\dots,h_k$ such that $h_1+\dots+h_k = n$ is known as a realization. The existence of realizations is a partially solved problem with a few general results for an…
Quantum trajectory methods can be used for a wide range of open quantum systems to solve the master equation by unraveling the density operator evolution into individual stochastic trajectories in Hilbert space. This C++ class library…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
WE use the structure theory for C_0 operators to determine when the square of a C_0(1) operator is irreducible and when its lattices of invariant and hyperinvariant subspaces coincide.
A $k$-net($n$) is a combinatorial design equivalent to $k-2$ mutually orthogonal Latin squares of order $n$. A relation in a net is a linear dependency over $\mathbb{F}_2$ in the incidence matrix of the net. A computational enumeration of…
A quantum Latin square of order $v$, QLS($v$), is a $v\times v$ array in which each of entries is a unit column vector from the Hilbert space $\mathbb{C}^{v}$, such that every row and column forms an orthonormal basis of $\mathbb{C}^{v}$.…