Robust quantum circuit for clique problem with intermediate qudits

Clique problem has a wide range of applications due to its pattern matching ability. There are various formulations clique like k-clique problem, maximum etc. The k-Clique determines whether an arbitrary network or not whereas finds the largest in graph. It is already exhibited literature that (NP-problem) can be solved asymptotically faster by using quantum algorithms compared conventional computing. Quantum computing with higher dimensions gaining popularity large storage capacity and computation power. In this article, we have shown improved circuit implementation for (MCP) help higher-dimensional intermediate temporary qudits first time best our knowledge. cost state-of-the-art colossal huge number n-qubit Toffoli gates. We depth over applying generalized gate decomposition ququarts (4-dimensional qudits).