Quantum Speedup for Inferring the Value of Each Bit of a Solution State in Unsorted Databases Using a Bio-Molecular Algorithm on IBM Quantum's Computers

In this paper, we propose a bio-molecular algorithm with O(n(2)) biological operations, O(2(n-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 2(n) items of n bits. We show that the value of each bit of the outcome is determined by executing our bio-molecular algorithm n times. Then, we show how to view a bio-molecular solution space with 2(n-1 )DNA 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-molecularsolution space with 2(n-1 )DNA strands. Next, we demonstratethat the value of each bit of the output solution can be determined by executing the proposed extended quantum algorithms n times. To verify our theorem, we find the maximum-sized clique to a graph with two vertices and one edge and the solution b that satisfies b(2) 1 (mod 15) and 1 < b < (15/2) using IBM Quantum's backend.

Automated summary

In this paper, a bio-molecular algorithm is proposed for inferring the value of a bit from an unsorted database. The algorithm determines the value of each bit by executing the algorithm multiple times and utilizes quantum algorithms to compute the unitary operator and eigenvalues for specific bits. The effectiveness of the algorithm is verified through experiments.