DNA, deoxyribonucleic acid, carrying encoded genetic information at molecular level, is the most significant discovery in the history of genetics. Previous researches on DNA included topics of bases, base-pairing, hydrogen bonds, structure, base sequence, dynamics, replication and mutation. DNA must duplicate itself, and so DNA structure and DNA replication are the fundamental problems. Watson and Crick described the structure and the mechanism for replication of DNA. Other authors focused their studies on DNA replication. DNA molecules are micro-entities ruled by laws of quantum mechanics, but the mechanisms, found previously of DNA forming and replicating, were not explored by applying quantum mechanics. Here we show that controlled by quantum mechanics, the quantum state of DNA is a bio-quantum-entangled state, the mechanism of DNA forming and replicating is a process of bio-quantum entangling, de-entangling and re-entangling. This bio-quantum mechanical result is different from the conventional biochemical descriptions of DNA structure and replication. DNA genetics is bio-quantum genetics in nature. With this deep understanding, reform and progress should be expected for further development of genetics.
In this paper, we propose a bio-molecular algorithm with O(${n}$2) biological operations, O(
2n−1) DNA strands, O(
n) tubes and the longest DNA strand, O(
n), for inferring the value of a bit from the only output satisfying any given condition in an unsorted database with
2nitems of
nbits. We show that the value of each bit of the outcome is determined by executing our bio-molecular algorithm
ntimes. Then, we show how to view a bio-molecular solution space with
2n-1DNA strands as an eigenvector and how to find the corresponding unitary operator and eigenvalues for inferring the value of a bit in the output. We also show that using an extension of the quantum phase estimation and quantum counting algorithms computes its unitary operator and eigenvalues from bio-molecular solution space with
2n-1DNA strands. Next, we demonstrate that the value of each bit of the output solution can be determined by executing the proposed extended quantum algorithms
ntimes. To verify our theorem, we find the maximum-sized clique to a graph with two vertices and one edge and the solution
bthat satisfies
b2≡1(mod 15) and
1<b<(15/2)using IBM Quantum’s backend.