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P-Adic Numbers Ultrametric Analysis and Applications

New quantum algorithm solving the NP complete problem

Makoto Ohya

Published Feb 1, 2012• 0 citations
Publisher

Abstract

We review the quantum chaos algorithm solving the NP-complete problems in polynomial time. This work has been done in the series of papers with Professor Igor Volovich for nearly ten years.
DOI
10.1134/s2070046612020082

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Ohya and Volovich found the quantum algorithm with a chaos dynamics, called the OV SAT algorithm which enabled to solve NP-Complete problem in polynomial time. It is proved that the unitary operator of the quantum algorithm can be constructed by a product of so called fundamental gates. To discuss the computational complexity rigorously, we intro- duced a generalized quantum Turing machine(GQTM) where the computational process is given by quantum channels including a dispative dynamics and the configuration is represented by density operators. In this paper, we explain the GQTM and the OV SAT algorithm, then we discuss the computational complexity of OV SAT algorithm. Finally, we introduce some resent results and topics by use of GQTM.
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