团问题生物分子解的量子计算机算法
Quantum Algorithms of Bio-molecular Solutions for the Clique Problem on a Quantum Computer
摘要：
本文证明了基于DNA的算法[Ho et al.2005]对任意一个n阶p边图G =（V，E）及其n阶m = 1的补图G1 =（V，E1）的团问题的一个实例的求解是有效的（n*（n-1））/2）-p）边可以通过Hadamard门、“非”门、C“非”门、CC“非”门、Grover算子和量子计算机上的量子测量来实现。证明了如果用Grover算法来完成DNA算法中的读出步骤，则DNA算法的量子实现等价于Grover算法语言中的预言工作，即Grover搜索步骤之前的目标状态标记.结果表明，一个预言机工作可以用O（（2 * n）*（n + 1）*（n + 2）/ 3）个“非”门、一个CNOT门和O（（4 * m）+（2 * n）*（n + 1）*（n + 14））/ 6）个CC“非”门来完成.这就是说，对于基于DNA的算法的量子实现[Ho et al. 2005]，可以更快地标记目标状态，这也意味着可以快速解决团问题的实例。
英文摘要：
In this paper, it is demonstrated that the DNA-based algorithm [Ho et al. 2005] for solving an instance of the clique problem to any a graph G = (V, E) with n vertices and p edges and its complementary graph G1 = (V, E1) with n vertices and m = (((n*(n-1))/2)-p) edges can be implemented by Hadamard gates, NOT gates, CNOT gates, CCNOT gates, Grover's operators, and quantum measurements on a quantum computer. It is also demonstrated that if Grovers algorithm is employed to accomplish the readout step in the DNA-based algorithm, the quantum implementation of the DNA-based algorithm is equivalent to the oracle work (in the language of Grover's algorithm), that is, the target state labeling preceding Grover,s searching steps. It is shown that one oracle work can be completed with O((2 * n) * (n + 1) * (n + 2) / 3) NOT gates, one CNOT gate and O((4 * m) + (((2 * n) * (n + 1) * (n + 14)) / 6)) CCNOT gates. This is to say that for the quantum implementation of the DNA-based algorithm [Ho et al. 2005] a faster labeling of the target state is attained, which also implies a speedy solution to an instance of the clique problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
