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2 International Journal of Applied Mathematics and Computer Science

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Noise effects in the quantum search algorithm from the viewpoint of computational complexity

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Gawron P. , Klamka J. , Winiarczyk R.

International Journal of Applied Mathematics and Computer Science

2012

tom 22

nr 2

493-499

We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on the computational complexity of the quantum search algorithm. We show that it is only for small amounts of noise that the quantum search algorithm is still more efficient than any classical algorithm.

Self-replication processes in nanosystems of informatics

100%

Węgrzyn S. , Winiarczyk R. , Znamirowski L.

International Journal of Applied Mathematics and Computer Science

2003

tom 13

nr 4

585-591

Recent research on the nanotechnological processes of molecular products and object synthesis as well as research on the nanosystems of informatics, stimulates the development of technical systems of informatics. Until now, they have been used mainly for computational tasks when, similarly to biological organisms, they allowed the development of self-replicating products and complete objects. One can focus here on the model of a circulation of materials, information and energy in a biological cell, and a model of the self-replication phenomenon. In the model of materials, information and energy circulation, we can distinguish a multi-phase process of creating products which are later used for object construction. The first phase is a translation process based on information from mRNA, while the next one consists of post-translational modifications based on environmental interactions. The self-replication model presented in this paper refers to a self-replication of a material object together with its internal software, which had determined the object creation. The presented models of materials, information and energy circulation in a biological cell together with models of the self-replication phenomenon can be a basis for the design and development of technical systems of informatics capable of creating self-replicating products and objects.