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.

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作业车间调度问题的变分量子算法案例研究

组合优化对旨在提高效率的大量工业流程进行建模。一般来说，准确地解决这类问题在计算上是难以处理的。因此，从业者依赖启发式解决方法。变分量子算法是优化启发式算法，可以使用可用的量子硬件进行演示。在本案例研究中，我们将在 IBM 的超导量子处理器上运行的四种变分量子启发式算法应用于作业车间调度问题。我们的问题优化了钢铁制造过程。对 5 个量子位的比较表明，最近的滤波变分量子特征求解器 (F-VQE) 收敛速度更快，并且比标准变分量子特征求解器 (VQE) 的量子近似优化算法 (QAOA) 更频繁地采样全局最优值，和变分量子虚时间演化（VarQITE）。此外，F-VQE 可以轻松解决硬件上多达 23 个量子位的问题，而无需进行错误缓解后处理。