In the Maximum Clique Problem, the objective is to find a clique whose size is maximum among all the cliques of an arbitrary undirected and unweighted graph. Maximum Clique Problem resembles with minimum vertex cover problem , independent set problem. As it is an NP-hard problem, no polynomial time algorithms can be found. As these problems have several important practical applications such as information retrieval, community detection in network, spatial data mining etc, it is of great interest to try to synthesis the circuit of Maximum Clique Problem. In classical computing any brute-force solution to the Maximum Clique Problem requires an exponential increase of time with the size of the problem (i.e., with time complexity of O(2^n)) . In this paper, Maximum Clique Problem has been solved using combinatorial approachof Grover's search algorithm . An algorithm has been proposed that auto-generates the circuit for any given undirected and unweighted graph  which makes the approach generalized in nature for Maximum Clique Problem. Computational speed up is achieved by using our approach with the help of quantum mechanical effect that is quantum superposition. We have simulated the proposed circuit using IBM 's QISkit platform and verified its correctness .
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 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) .
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In the Maximum Clique Problem, the objective is to find a clique whose size is maximum among all the cliques of an arbitrary undirected and unweighted graph. Maximum Clique Problem resembles with minimum vertex cover problem , independent set problem. As it is an NP-hard problem, no polynomial time algorithms can be found. As these problems have several important practical applications such as information retrieval, community detection in network, spatial data mining etc, it is of great interest to try to synthesis the circuit of Maximum Clique Problem. In classical computing any brute-force solution to the Maximum Clique Problem requires an exponential increase of time with the size of the problem (i.e., with time complexity of O(2^n))
Clique problem has several applications in computer vision, automatic test pattern generation, predicting protein structures, and many kinds of such pattern search
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Maximum Clique Problem has been solved using combinatorial approachof Grover's search algorithm . An
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
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proposed that auto-generates the
reduced to O(\sqrt{2^{k*log_2n
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,
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for Maximum Clique Problem. Computational speed up is achieved by using our approach with the help of quantum mechanical effect that is quantum superposition. We have simulated the proposed circuit using IBM 's QISkit platform and verified its correctness
. 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)