Variational Algorithms for Workflow Scheduling Problem in Gate-Based Quantum Devices

In this paper we consider the combinatorial optimization problem known as workflow scheduling. We compare three encoding schemes of varying density: one-hot, binary, and domain wall, test their performance against two well-known hybrid quantum-classical algorithms: Quantum Approximate Optimization Algorithm (QAOA) Variational Eigensolver (VQE). an attempt to obtain best results possible, investigate various parameters algorithms out other state-of-the-art improvements, such dedicated QAOA mixers. Ultimately, prove that, despite its popularity, one-hot is not always best, using a denser scheme, binary or can allow for solving larger instances Additionally, combining above-mentioned encodings with mixers reduces number infeasible solutions, leading better results.