团问题的电路设计及其在量子计算机上的实现
Circuit Design for Clique Problem and Its Implementation on Quantum Computer
摘要：
在图中查找团具有模式匹配能力的几个应用。$k$ -团问题是团问题的一种特殊情况，它决定了任意图是否包含一个大小为$k$的团，已经在量子领域得到了解决。$k$的变体-列出所有大小为$k$的派系问题，也是当今流行的应用程序。尽管如此，在量子环境中实现这种$k$ -团问题的变体仍然没有被触及。在本文中，除了这种$k$ -团问题的理论解决方案，实际的量子门为基础的实现已解决使用Grover的算法。该方法被进一步推广到经典-量子混合结构中最大团问题的电路设计。对于任意给定的无向无权图和任意给定的$k$，该算法都能自动生成回路，这使得我们的方法在本质上具有推广性。对于相对于大图的小$k$，与最先进的方法相比，所提出的解决$k$-团问题的方法显示出量子位成本和电路深度的降低。提出了一个将团问题的自动生成电路映射到量子器件的框架。实验结果的分析表明，使用IBM的Qiskit。
英文摘要：
Finding cliques in a graph has several applications for its pattern matching ability. $k$-clique problem, a special case of clique problem, determines whether an arbitrary graph contains a clique of size $k$, has already been addressed in quantum domain. A variant of $k$-clique problem that lists all cliques of size $k$, has also popular modern-day applications. Albeit, the implementation of such variant of $k$-clique problem in quantum setting still remains untouched. In this paper, apart from theoretical solution of such $k$-clique problem, practical quantum gate-based implementation has been addressed using Grover's algorithm. This approach is further extended to design circuit for the maximum clique problem in classical-quantum hybrid architecture. The algorithm automatically generates the circuit for any given undirected and unweighted graph and any given $k$, which makes our approach generalized in nature. The proposed approach of solving $k$-clique problem has exhibited a reduction of qubit cost and circuit depth as compared to the state-of-the-art approach, for a small $k$ with respect to a large graph. A framework that can map the automated generated circuit for clique problem to quantum devices is also proposed. An analysis of the experimental results is demonstrated using IBM's Qiskit.
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