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A New Quantum Algorithm for NP-complete Problems

Makoto Ohya, Masanori Ohya, Igor V. Volovich

Published Jan 1, 2002• 1 citation
OpenAlex

Abstract

An approach to the solution of NP-complete problems based on quantum computing and chaotic dynamics is proposed. We consider the satisfiability problem and argue that the problem, in principle, can be solved in polynomial time if we combine the quantum computer with the chaotic dynamics amplifier based on the logistic map.

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An approach to the solution of NP-complete problems based on quantum computing and chaotic dynamics is proposed. We consider the satisfiability problem and argue that the problem, in principle, can be solved in polynomial time if we combine the quantum computer with the chaotic dynamics amplifier based on the logistic map. We discuss a possible implementation of such a chaotic quantum computation by using the atomic quantum computer with quantum gates described by the Hartree-Fock equations. In this case, in principle, one can build not only standard linear quantum gates but also nonlinear gates and moreover they obey to Fermi statistics. This new type of entaglement related with Fermi statistics can be interesting also for quantum communication theory.
Hamilton loop problem belongs to NP-complete problems.This paper proposed an approach to it based on quantum computation and chaotic dynamics.Firstly,using a Boolean polynomial analyzed the Hamilton loop problem.Secondly,constructed a novel model based on quantum computation and chaotic dynamics which using a chaotic dynamics amplifier amplified the initial value in polynomial time.Considered the Hamilton loop problem and argued that the problem,in principle,it could be solved in polynomial time if the quantum computer was combined with the chaotic dynamics amplifier based on the logistic map.
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. keywords: Quantum Algorithm, NP-complete problem, Chaotic Dynamics 1
A novel learning policy in multi-agent reinforcement learning is presented, trying to find another tradeoff of exploration and exploitation efficiently, It use the output of the classical quantum computer as an input for chaotic dynamics amplifier, The novel amplifier consider the chaotic effect, it can amplify the initial value in polynomial time. It considers the action selection problem and argues that the problem, in principle, can be solved in polynomial time if it combines the quantum computer with the chaotic dynamics amplifier based on the logistic map.