IEEE Trans Nanobioscience. 2022 Apr;21(2):286-293. doi: 10.1109/TNB.2021.3130811. Epub 2022 Mar 31.
In this paper, we propose a bio-molecular algorithm with O( n ) biological operations, O( 2 ) 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 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 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-molecular solution space with 2 DNA strands. Next, we demonstrate that 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 ≡ 1 (mod 15) and using IBM Quantum's backend.
在本文中，我们提出了一种具有 O( n )个生物操作、O( 2 )个 DNA 链、O( n )个管和最长 DNA 链 O( n )的生物分子算法，用于从包含 2 项 n 位的未排序数据库中唯一满足给定条件的输出推断出一位的值。我们证明了输出中每个位的值是通过执行我们的生物分子算法 n 次来确定的。然后，我们展示了如何将具有 2 个 DNA 链的生物分子解决方案空间视为特征向量，以及如何找到相应的幺正算子和特征值来推断输出中一位的值。我们还表明，使用量子相位估计和量子计数算法的扩展可以从具有 2 个 DNA 链的生物分子解决方案空间计算其幺正算子和特征值。接下来，我们证明了输出解决方案中每个位的值可以通过执行所提出的扩展量子算法 n 次来确定。为了验证我们的定理，我们找到了具有两个顶点和一条边的图的最大团和满足 b ≡ 1 (mod 15)的解 b，并使用了 IBM Quantum 的后端。
