Quantum Logical Bioinformatics: The Genetic Alphabet of 4 Unitary Hadamard Operators and Cyclic Groups

This paper presents data on an additional operator-alphabetic informatic system for biological inheritance in living organisms, which can provide inheritance of biological algorithms and functions and which exists alongside the well-known nucleotide-alphabetic system of information inheritance. This operator-alphabetic bioinformatics and its alphabet are linked to quantum mechanics, quantum logic, and quantum information science, since genetic molecules belong to the microworld of quantum mechanics. In the search for and justification of this operator bioinformatics and its alphabets, special attention is paid to unitary operators, which underlie all calculations in quantum computers and which, in quantum mechanics, describe the evolution of closed quantum systems. The quantum logic apparat being developed for this bioinformatics is based on a genetic alphabet of four unitary Hadamard matrices, families of unitary matrices based on this alphabet, and cyclic groups of unitary transformations. Some prospects of the proposed approach for the development of quantum logic biology, artificial intelligence, and biotechnology are discussed.