Hybrid Quantum Approximate Algorithms for Solving Flow Shop Scheduling Problem

There is currently a large gap between the theoretical advantages of quantum computing and the practical use of quantum computers. This is due to the small number of qubits currently available. Rapid technological progress allows us to assume that in the near future, it will be possible to solve problems that are currently a challenge for algorithms running on classical computers. Using the example of an NP-hard flow problem, we present the application of the Qiskit optimization package performed on an IBM quantum computer. This problem is well-studied in classical computing, important for theoretical and practical reasons. The use of quantum optimization will undoubtedly affect the more efficient use of many resources in management, production, logistics, and medicine (duty plans, classification problems, etc.).