Related papers: Theoretical Aspects of the SOM Algorithm
This is continuation of the approach to performing quantum algorithms using geometric structures which was presented by Aerts and Czachor. We solve the Simon's problem which, next to the Shor's alghorithm, is a representative of a quantum…
A series of recent papers raises worries about the manipulative potential of algorithmic transparency. But while the concern is apt and relevant, it is based on a fraught understanding of manipulation. Therefore, this paper draws attention…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.
This is a brief review of the experimental and theoretical quantum computing. The hopes for eventually building a useful quantum computer rely entirely on the so-called "threshold theorem". In turn, this theorem is based on a number of…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed.…
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
Shor's algorithm is examined critically from the standpoint of it's eventual use to obtain the factors of large integers.
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…
We discuss some seemingly paradoxical yet valid effects of quantum physics in information processing. Firstly, we argue that the act of ``doing nothing'' on part of an entangled quantum system is a highly non-trivial operation and that it…
We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small…
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 new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
Holographic algorithms are a recent breakthrough in computer science and has found applications in information theory. This paper provides a proof to the central component of holographic algorithms, namely, the Holant theorem. Compared with…
We give an endorsement for Cornacchia's famous algorithm. Thus we do not claim anything new but an approach which is supposed to be simpler than those of previous works written with the same aim.