A Simplified Quantum Approach Using Grover's Algorithm for Solving the Vertex Cover Problem

Quantum computing offers an accelerated mechanism for solving combinatorial optimization problems that could be hardly solvable with classical tools, in this context, this paper highlights the utility of quantum computing in solving NP-complete problems efficiently and shows up the importance of employing quantum algorithms achieving parallel calculation in the purpose of reducing the algorithmic complexity and simplifying the development of optimization applications. Within this publication, an optimized version of quantum circuit conception for developing the oracle of the Grover's search algorithm is introduced for solving the vertex cover problem, and it was also tested using the Qiskit library and applied to a set of instances to evaluate its performance.