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

Non-Abelian Monopole in the Parameter Space of Point-like Interactions

We study non-Abelian geometric phase in $\mathscr{N} = 2$ supersymmetric quantum mechanics for a free particle on a circle with two point-like interactions at antipodal points. We show that non-Abelian Berry's connection is that of $SU(2)$ magnetic monopole discovered by Moody, Shapere and Wilczek in the context of adiabatic decoupling limit of diatomic molecule.Comment: 15 pages, 3 tikz figures; minor correction