使用一种适用于量子的分支定界方法求解QUBO问题
Solving QUBOs with a quantum-amenable branch and bound method
AI总结：
本文提出并验证了一种适用于量子加速的精确经典分支定界QUBO求解器，结合高性能计算与运筹学技术提升性能，并与现有求解器进行了广泛对比分析。
摘要：
由于量子与经典时钟速度之间预期存在差异，分支定界算法的量子优势更有可能在涉及大型搜索树和低算子评估成本的环境中获得。因此，本文描述并实验验证了一种精确的经典分支定界求解器，用于求解无约束二次二值优化（QUBO）问题，该求解器符合上述标准。我们的求解器利用了文献中先前为Ising模型提出的低成本界限，包括Hartwig、Daske和Kobe于1984年提出的界限。我们详细介绍了用于提升求解器性能的来自高性能计算和运筹学的多种技术，包括全局变量重排序启发式方法、基于模拟退火的原始启发式方法以及递归界限的截断计算。我们还概述了多种简单且低成本的界限外推技术。最后，我们对求解器进行了广泛的实证分析，将其性能与最先进的QUBO和MaxCut求解器进行了比较，并讨论了通过量子分支定界实现加速所面临的挑战，这些挑战超越了任何二次量子加速所面临的困难。
英文摘要：
Due to the expected disparity in quantum vs. classical clock speeds, quantum advantage for branch and bound algorithms is more likely achievable in settings involving large search trees and low operator evaluation costs. Therefore, in this paper, we describe and experimentally validate an exact classical branch and bound solver for quadratic unconstrained binary optimization (QUBO) problems that matches these criteria. Our solver leverages cheap-to-implement bounds from the literature previously proposed for Ising models, including that of Hartwig, Daske, and Kobe from 1984. We detail a variety of techniques from high-performance computing and operations research used to boost solver performance, including a global variable reordering heuristic, a primal heuristic based on simulated annealing, and a truncated computation of the recursive bound. We also outline a number of simple and inexpensive bound extrapolation techniques. Finally, we conduct an extensive empirical analysis of our solver, comparing its performance to state-of-the-art QUBO and MaxCut solvers, and discuss the challenges of a speedup via quantum branch and bound beyond those faced by any quadratic quantum speedup.
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。
