Virtuous Quantum Heuristics for Combinatorial optimization

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

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 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 optimizationalgorithm (qaoa), the standard variational quantum eigensolver (vqe), and the standard variational quantum imaginary time evolution (varqite).Furthermore, the recent filtering variational quantum eigensolver (f-vqe) solves problem sizes of up to 23 qubits on hardware without errormitigation post processing.Combining f-vqe with error mitigation and causalcones could allow quantum optimization heuristics to scale to relevant problem sizes.