Exploring the Potential of the Filtering Variational Quantum Eigensolver

Kurzfassung

Job scheduling is a complex optimization problem with multiple variables, constraints, and goals. Solving such problems using classical computing can be challenging, since they are NP-complete and real-world instances can be quite large. Quantum computing is a promising solution, as it is theoretically faster than classical computing for certain types of problems. In this thesis, we use the filtering variational quantum eigensolver (F-VQE), a parameterized quantum algorithm, to solve a simplified real-world scheduling problem. The F-VQE algorithm optimizes solutions by filtering out unpromising ones and using a classical optimization routine to refine the remaining solutions. Although the F-VQE algorithm is based on a paper by Amaro et al. [AMR+22], it has not yet been fully evaluated for solving scheduling problems. While VQEs have been successful in solving combinatorial optimization problems, we seek to assess the performance of F-VQE in solving scheduling problems. We have two objectives in this research: firstly, to enhance and analyze the F-VQE algorithm, and secondly, to evaluate the potential of quantum computing in solving complex scheduling problems. To accomplish this, we will compare the performance of the F-VQE algorithm with other quantum and classical approaches for solving real-world scheduling problems. This will provide valuable insights into the effectiveness of quantum computing for solving these problems, as well as identify potential improvements to the F-VQE algorithm. We delve deeper into the F-VQE algorithm to identify potential areas for improvement. We will examine various ansatz designs, different filtering strategies, and encoding techniques. Worthwhile additions are implemented and tested against. To compare the F-VQE algorithm’s performance with other variational quantum algorithms and an approach using Grover’s algorithm, which is already implemented by the DLR. We evaluate the efficiency, scalability, and quality of solutions provided by each algorithm and discuss the potential benefits and drawbacks of the F-VQE for solving real-world scheduling problems.