作业车间调度问题的高效编码及其在量子计算机上的应用

IF 5.6 2区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Quantum Science and Technology Pub Date : 2024-12-23 DOI:10.1088/2058-9565/ad9cba
Mathias Schmid, Sarah Braun, Rudolf Sollacher and Michael J Hartman
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引用次数: 0

摘要

组合优化问题被认为是一种应用,量子计算可以产生变革性的影响。在工业环境中,作业车间调度问题的目标是为一组要在一组机器上运行的一组作业找到最佳调度,这是一个非常有趣的问题。在这里,我们引入了作业车间调度问题的有效编码,它比以前使用的编码需要更少的位串来计数所有可能的调度。对于由N个作业和N个操作组成的问题,与时间索引编码相比,所需的位串数量至少减少了一个因子。这对于解决量子计算机上的作业车间调度问题特别有益,因为需要更少的量子位来表示问题。我们的方法适用于大量灵活和常见的作业车间调度问题,其中操作可能在多台机器上执行。使用变分量子算法,我们证明了我们引入的编码比以前考虑的策略显著提高了量子算法的性能。重要的是,我们开发的编码还可以实现更紧凑的经典表示,因此将非常有用,甚至超出量子硬件的适用性。
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Highly efficient encoding for job-shop scheduling problems and its application on quantum computers
Combinatorial optimization problems are considered to be an application, where quantum computing can have transformative impact. In the industrial context, job shop scheduling problems that aim at finding the optimal schedule for a set of jobs to be run on a set of machines are of immense interest. Here we introduce an efficient encoding of job shop scheduling problems, which requires much fewer bit-strings for counting all possible schedules than previously employed encodings. For problems consisting of N jobs with N operations, the number of required bit-strings is at least reduced by a factor as compared to time indexed encodings. This is particularly beneficial for solving job shop scheduling problems on quantum computers, since much fewer qubits are needed to represent the problem. Our approach applies to the large class of flexible and usual job-shop scheduling problems, where operations can possibly be executed on multiple machines. Using variational quantum algorithms, we show that the encoding we introduce leads to significantly better performance of quantum algorithms than previously considered strategies. Importantly, the encoding we develop also enables significantly more compact classical representations and will therefore be highly useful even beyond applicability on quantum hardware.
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来源期刊
Quantum Science and Technology
Quantum Science and Technology Materials Science-Materials Science (miscellaneous)
CiteScore
11.20
自引率
3.00%
发文量
133
期刊介绍: Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics. Quantum Science and Technology is a new multidisciplinary, electronic-only journal, devoted to publishing research of the highest quality and impact covering theoretical and experimental advances in the fundamental science and application of all quantum-enabled technologies.
期刊最新文献
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