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.

翻译：在图形中查找 cliques 有几个应用程序来匹配其模式匹配能力。 $k$- clique 问题, 是一个特殊 clque 问题, 确定任意的图形是否包含一个大小为$k$的区块, 这个问题已经在量子域内得到解决 。 一个列出所有大小为$k$的区块的区块问题的变种方案, 也具有现代应用的流行性 。 尽管在量子设置中实施这种K$- clique 问题的变种, 仍然没有被触及 。 在本文中, 除了使用 Grover 的算法, 实际的量子门法实施已经解决了。 这个方法被进一步扩展到用于设计经典- quantum 混合结构中的最大结块问题的电路圈设计 。 算法自动生成任何给定的无方向和未加权的图形和任何给定的美元, 使得我们的方法具有普遍性。 与 量子设置的 量子- 问题解决 Qbit 成本和电路深度比 方法比, 与 状态- Q- 门基 法 法 方法已经用 Grover 法 方法解决了 。 对于一个小的 美元- crequemaclus 分析, 和 的 比例 比例 分析也是 的 的 的 的 的 磁路路路段 分析 的 。