Molecular solution for the subset-sum problem on DNA based quantum computing

Feynman in 1961 and in 1982 respectively proposed molecular computation and one of the most important problems in computation theory, that is, whether computing devices based on quantum theory are able to finish computations faster than the standard Turing machines. In 1994, Adleman succeeded to solve an instance of the Hamiltonian path problem in a test tube, just by handling DNA strands. Deutsch denoted a general model of quantum computation - the quantum Turing machine. Molecular solution for the subset-sum problem on DNA based supercomputing has been offered in Weng-long Chang et al. 2003 articles. Here, it is demonstrated that the DNA-based algorithm of an n-bit parallel adder and a DNA based algorithm of an n-bit parallel comparator to formally verify our designed molecular solutions for the subset-sum problem can be implemented by Hadamard gates, NOT gates, CNOT gates, CCNOT gates, Grovers operators, and quantum measurements on a quantum computer.