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 problemhas 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 . 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 (IBMQX architecture) .
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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Clique problem
Finding cliques in a graph
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in computer vision, automatic test pattern generation, predicting protein structures, and many kinds of such pattern search
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
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a generalized algorithm for the k-Clique problemhas been newly proposed using a classical-quantum hybrid approach , which can also be extended as a generalized algorithm for
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
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. The complexity of the proposed algorithm has been reduced to O(\sqrt{2^{k*log_2n
in classical-quantum hybrid architecture
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and any given k
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the
our
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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 (IBMQX architecture)
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