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Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to…
In this paper, we present a new approach to linearizing zero-one quadratic minimization problem which has many applications in computer science and communications. Our algorithm is based on the observation that the quadratic term of…
Quantum magic squares were recently introduced as a 'magical' combination of quantum measurements. In contrast to quantum measurements, they cannot be purified (i.e. dilated to a quantum permutation matrix) -- only the so-called…
In the classical theory of cubic interpolation splines there exists an algorithm which works with only $O\left( n\right)$ arithmetic operations. Also, the smoothing cubic splines may be computed via the algorithm of Reinsch which reduces…
When implementing functionality which requires sparse matrices, there are numerous storage formats to choose from, each with advantages and disadvantages. To achieve good performance, several formats may need to be used in one program,…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
We consider the solution of nonlinear equations in one real variable, the problem usually called by root finding. Although this is an old problem, we believe that some aspects of its solution using interval arithmetic are not well…
A procedure that generates parallelograms from any quadrilateral is presented. If the original quadrilateral is itself a parallelogram, then the procedure gives squares. Hence, when applied two times, this procedure generates squares from…
Reversible algorithms play a crucial role both in classical and quantum computation. While for a classical bit the only nontrivial reversible operation is the bit-flip, nature is far more versatile in what it allows to do to a quantum bit.…
Let $T = (T^{\textstyle \ast}, T^{\scriptscriptstyle \triangle})$ be a spherical latin bitrade. With each $a=(a_1,a_2,a_3)\in T^{\textstyle \ast}$ associate a set of linear equations $\eq(T,a)$ of the form $b_1+b_2=b_3$, where $b =…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…
Processors may find some elementary operations to be faster than the others. Although an operation may be conceptually as simple as some other operation, the processing speeds of the two can vary. A clever programmer will always try to…
This paper makes three contributions to estimating the number of perfect matching in bipartite graphs. First, we prove that the popular sequential importance sampling algorithm works in polynomial time for dense bipartite graphs. More…
Machine-learning tasks frequently involve problems of manipulating and classifying large numbers of vectors in high-dimensional spaces. Classical algorithms for solving such problems typically take time polynomial in the number of vectors…
Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
A multi-latin square of order $n$ and index $k$ is an $n\times n$ array of multisets, each of cardinality $k$, such that each symbol from a fixed set of size $n$ occurs $k$ times in each row and $k$ times in each column. A multi-latin…
We show how to generate an expression for the number of k-line Latin rectangles for any k. The computational complexity of the resulting expression, as measured by the number of additions and multiplications required to evaluate it, is on…
A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.