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IOP Conference Series Materials Science and Engineering

Genetic alphabets, unitary matrixes and quantum-algorithmic genetics

Sergey Valentinovich Petoukhov, Elena S. Petukhova, Vitaly I. Svirin

Published Mar 26, 2019• 2 citations
Publisher

Abstract

Unitary operators are the basis of all calculations in quantum computers and play an important role in quantum mechanics. The presented results show that matrix forms of representation of structured DNA and RNA alphabets can be considered as a set of sparse unitary matrices. These results are useful for the development of models of quantum-algorithmic genetics, from the point of view of which living organisms are quantum-information entities.

DOI
10.1088/1757-899x/489/1/012048

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Unitary operators are the basis of all calculations in quantum computers and play an important role in quantum mechanics. The presented results show that matrix forms of representation of structured DNA and RNA alphabets can be considered as a set of sparse unitary matrices. These results are useful for the development of models of quantum-algorithmic genetics, from the point of view of which living organisms are quantum-information entities.
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Replication of DNA and synthesis of proteins are studied from the view-point of quantum database search. Identification of a base-pairing with a quantum query gives a natural (and first ever!) explanation of why living organisms have 4 nucleotide bases and 20 amino acids. It is amazing that these numbers arise as solutions to an optimisation problem. Components of the DNA structure which implement Grovers algorithm are identified, and a physical scenario is presented for the execution of the quantum algorithm. It is proposed that enzymes play a crucial role in maintaining quantum coherence of the process. Experimental tests that can verify this scenario are pointed out.
Molecules are the basis of life. They can consider as a quantum system. So it is necessary to enter quantum mechanics in biological discussion. Specifically, we should expect the quantum to be the basis for heredity, genetic, biology and DNA. In this paper we consider the DNA molecules as a quantum system. We discuss about the relation between the heredity, biology and DNA and quantum systems. We also claim that there is a relation between the quantum information and some biologicaly-process such as cell division, cloning so that we think that the root of all problems in cloning may be in the quantum effects.
Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors), and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i) storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii) replication errors introduced during DNA replication process, (iii) transcription errors introduced during DNA to mRNA transcription, and (iv) translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.
The solution of sets of linear simultaneous equations can be accomplished using matrices and we show how this is done. In quantum computation, matrices ‘operate’ or act on vectors to move a system from one quantum state to another as it evolves with time. The solution of sets of linear simultaneous equations can be accomplished using matrices and we show how this is done. Matrices can also be used to perform transformations of points in two- and three-dimensional space through rotations and reflections. Self-adjoint matrices play an important role in quantum computation because, as we shall see, they have real eigenvalues which correspond to the measured values of quantum observables. The procedure for calculating the inverse of a general n×n matrix necessitates the introduction of some new terminology. The rows of a unitary matrix are pairwise orthogonal so that the inner product of two distinct rows will be zero.