On Genetic Unitary Matrices and Quantum-Algorithmic Genetics

Abstract

The article is devoted to parallelisms between the structural organization of the molecular genetic system and mathematics of quantum computers. This mathematics is perspective for developing systems of artificial intelligence. Using this mathematics to study, the genetic system can reveal bioinformational patents of the living nature for scientific and technologic progress. Unitary matrices are the basis of all calculations in quantum computers. Our described results show that structured systems of molecular genetic alphabets in their matrix forms of representations can be considered as sets of sparse unitary matrices related with phenomenologic features of the degeneracy of the genetic code. These sparse unitary matrices have orthogonal systems of functions in their rows and columns. A complementarity exists among some unitary genetic matrices in relation to each other. Tensor (or Kronecker) families of unitary genetic matrices with their fractal-like properties are also considered. These new results are interesting for development of quantum-algorithmic genetics and for revealing fundamental principles of bioinformatics.