Clique problem has several applications in computer vision, automatic test pattern generation, predicting protein structures, and many kinds of such pattern search. In this paper, a generalized algorithm for the k-Clique problem has been newly proposed using a classical-quantum hybrid approach, which can also be extended as a generalized algorithm for maximum clique problem. The complexity of the proposed algorithm has been reduced to $O(\sqrt{2^{k*log_2n}})$ than the classical algorithm with complexity $O(2^n)$ for a k sized clique in an n node graph. The algorithm automatically generates the circuit for any given undirected and unweighted graph, which makes the approach generalized in nature. The experimental result of the generic algorithm has been implemented in the $IBMQ\_Qasm\_Simulator$. The generated circuit can also be mapped in Noisy Intermediate-Scale Quantum (NISQ) devices(IBM QX architecture).

翻译： clique 问题在计算机视觉、 自动测试模式生成、 预测蛋白质结构以及许多类型的模式搜索中有若干应用。 在本文中, 使用古典- 量子混合法新提出了 k- 量子问题通用算法, 也可以作为最大分层问题通用算法加以扩展。 提议的算法的复杂性已经降低到$O( sqrt{2 ⁇ k*log_ 2n ⁇ ), 而不是用于n节点图中的 k 尺寸分类的复杂典型算法$( 2 ⁇ n) 。 算法自动生成任何给定的无方向和无加权的图的电路, 使该方法具有普遍性。 通用算法的实验结果已经在 $IBM ⁇ sm ⁇ ⁇ Simulator$中实施。 生成的电路也可以在 Nisy 中级量子设备( IBM QX 结构) 中绘制。