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

TL;DR

This paper explores the application of four variational quantum algorithms to a real-world job shop scheduling problem in steel manufacturing, demonstrating that F-VQE outperforms other heuristics on IBM quantum hardware.

Contribution

It provides a comparative analysis of variational quantum heuristics for industrial scheduling, highlighting F-VQE's superior convergence and scalability on current quantum processors.

Findings

F-VQE converges faster than QAOA, VQE, and VarQITE.

F-VQE more frequently finds the global optimum.

F-VQE can solve up to 23 qubits on hardware without error mitigation.

Abstract

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.