约束优化方法通过量子就绪方法提供优越的图划分经典性能
Constrained-optimization Approach Delivers Superior Classical Performance for Graph Partitioning via Quantum-ready Method
摘要：
图划分是一组重要的著名的计算密集型（NP-难）图问题，转移到离散约束优化。我们通过两种不同的量子就绪方法对问题的解决方案进行了抽样，以了解每种方法的优缺点。首先，我们制定和采样的问题作为一个二次无约束二进制优化（QUBO）的问题，通过最著名的QUBO制定，使用一流的QUBO采样器运行纯粹的经典。其次，我们在更高的层次上将问题公式化为一组约束和一个目标函数，并使用约束优化采样器对其进行采样（该采样器通过QUBO对问题进行内部采样，也是经典采样）。我们发现，这两种方法往往提供更好的分区比专用的经典图分区。此外，我们发现，约束优化方法往往能够提供更好的分区在更短的时间比定制QUBO方法，没有知识的图形分区问题。从图划分本身退一步，一个关键的争议问题是定制算法或通用工具是否更有可能向现实世界的用户提供QC的功能。这些结果与这个问题有关，尽管它们需要对其他问题和情况进行确认，以及由QC更换低水平采样器。尽管如此，这些早期证据仍然支持这样一种观点，即通用工具将对一系列问题做出重大贡献，扩大QC的影响。这种好处与所使用的低级采样器无关，无论是软件还是QC，因此需要在高级优化方面做更多的工作。这种软件的早期版本现在已经在云中商用，为某些问题提供了卓越的经典性能，使量子向前组织现在能够迁移到量子就绪方法。
英文摘要：
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to understand the pros and cons of each method. First we formulated and sampled the problem as a quadratic unconstrained binary optimization (QUBO) problem, via the best known QUBO formulation, using a best-in-class QUBO sampler running purely classically. Second, we formulated the problem at a higher level, as a set of constraints and an objective function, and sampled it with a constrained-optimization sampler (which internally samples the problem via QUBOs also sampled classically). We find that both approaches often deliver better partitions than the purpose-built classical graph partitioners. Further, we find that the constrained-optimization approach is often able to deliver better partitions in less time than the bespoke-QUBO approach, without knowledge of the graph-partitioning problem. Stepping back from graph partitioning itself, one key controversial question is whether bespoke algorithms or general tools are more likely to deliver the power of QCs to real-world users. These results bear on that question, though they require confirmation on other problems and instances as well as replacement of the low-level sampler by a QC. Still, this early evidence supports the proposition that general tools will contribute significantly to a range of problems, expanding the impact of QCs. This benefit is independent of the low-level sampler employed, whether software or QC, so reinforces the need for more work on high-level optimization. An early version of such software is commercially available in the cloud today, delivering superior classical performance for some problems, enables quantum-forward organizations to migrate to quantum-ready methods now.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
