A case study of variational quantum algorithms for a job shop scheduling problem

• Published in: EPJ quantum technology Vol. 9; no. 1
• Main Authors: Amaro, David, Rosenkranz, Matthias, Fitzpatrick, Nathan, Hirano, Koji, Fiorentini, Mattia
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2022; Springer Nature B.V
• Subjects: Algorithms; Case studies; Combinatorial analysis; Hardware; Job shop scheduling; Job shops; Nanotechnology and Microengineering; Optimization; Physics; Physics and Astronomy; Quantum Information Technology; Quantum Physics; Qubits (quantum computing); Special Issue on Quantum Industry; Spintronics; Steel making; Quantum hardware; Variational quantum algorithms; Combinatorial optimization; Heuristics
• ISSN: 2662-4400; 2196-0763
• DOI: 10.1140/epjqt/s40507-022-00123-4

Combinatorial optimization models a vast range of industrial processes aiming at improving their efficiency. In general, solving this type of problem exactly is computationally intractable. Therefore, practitioners rely on heuristic solution approaches. Variational quantum algorithms are optimization heuristics that can be demonstrated with available quantum hardware. In this case study, we apply four variational quantum heuristics running on IBM’s superconducting quantum processors to the job shop scheduling problem. Our problem optimizes a steel manufacturing process. A comparison on 5 qubits shows that the recent filtering variational quantum eigensolver (F-VQE) converges faster and samples the global optimum more frequently than the quantum approximate optimization algorithm (QAOA), the standard variational quantum eigensolver (VQE), and variational quantum imaginary time evolution (VarQITE). Furthermore, F-VQE readily solves problem sizes of up to 23 qubits on hardware without error mitigation post processing.