A stochastic limit approach to the SAT problem

We propose a new approach to solve an NP complete problem by means of stochastic limit.Comment: 8 page

Quantum Algorithm for SAT Problem and Quantum Mutual Entropy

It is von Neumann who opened the window for today's Information epoch. He defined quantum entropy including Shannon's information more than 20 years ahead of Shannon, and he introduced a concept what computation means mathematically. In this paper I will report two works that we have recently done, one of which is on quantum algorithum in generalized sense solving the SAT problem (one of NP complete problems) and another is on quantum mutual entropy properly describing quantum communication processes.Comment: 19 pages, Proceedings of the von Neumann Centennial Conference: Linear Operators and Foundations of Quantum Mechanics, Budapest, Hungary, 15-20 October, 200

New quantum algorithm for studying NP-complete problems

Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm which is a combination of the ordinary quantum algorithm with a chaotic dynamical system. We consider the satisfiability problem as an example of NP-complete problems and argue that the problem, in principle, can be solved in polynomial time by using our new quantum algorithm.Comment: 11 pages, 1 figur

A Generalization of Grover's Algorithm

We investigate the necessary and sufficient conditions in order that a unitary operator can amplify a pre-assigned component relative to a particular basis of a generic vector at the expense of the other components. This leads to a general method which allows, given a vector and one of its components we want to amplify, to choose the optimal unitary operator which realizes that goal. Grover's quantum algorithm is shown to be a particular case of our general method. However the general structure of the unitary we find is remarkably similar to that of Grover's one: a sign flip of one component combined with a reflection with respect to a vector. In Grover's case this vector is fixed; in our case it depends on a parameter and this allows optimization.Comment: 20 pages, no figure

A parallel spatial quantum search algorithm applied to the 3-SAT problem

This work presents a quantum search algorithm to solve the 3-SAT problem. An improvement over one of the best known classical algorithms for this problem is proposed, replacing the local search with a quantum search algorithm. The performance of the improved algorithm is assessed by simulating it using parallel programming techniques with shared memory. The experimental analysis demonstrate that the parallel simulation of the algorithm takes advantage of the available computing resources to improve over the eficiency of the sequential version, thus allowing to perform realistic simulations in reduced execution times.Sociedad Argentina de Informática e Investigación Operativ