论文标题
比较量子和经典算法的最大2-SAT问题实例的硬度
Comparing the hardness of MAX 2-SAT problem instances for quantum and classical algorithms
论文作者
论文摘要
针对特定问题的算法可能会发现问题的某些实例更容易,而对于固定的输入大小也更难解决。我们通过数值分析了各种连续时间量子算法和类似的经典算法的最大2-SAT问题实例的相对硬度。这有两个动机:调查在基准测试目的的量子算法的数值模拟中通常使用的小型问题实例是否是在较大实例方面的良好表示,在其硬度方面的硬度方面是一个较大实例,并确定我们在varriative variviation in in Instrith in in Instrith in in Instrith in in Instrith in in Instrith中的持续量子算法的适用性。我们发现,尽管所有考虑的算法之间存在相关性,但它们似乎足够虚弱,以至于在实践中可能需要一种投资组合方法。我们的结果还表明,随着问题大小的增加,随机生成的实例的硬度范围不断扩大,这既表明了小规模的硬度分布的差异,又表明了投资组合方法的价值,可以减少极限实例的数量。我们确定了这些量子算法的特定弱点,这些量子算法可以通过投资组合方法克服这些算法,从而无法有效地解决令人满意的实例(这很容易经典)。
An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyse the relative hardness of MAX 2-SAT problem instances for various continuous-time quantum algorithms and a comparable classical algorithm. This has two motivations: to investigate whether small-sized problem instances, which are commonly used in numerical simulations of quantum algorithms for benchmarking purposes, are a good representation of larger instances in terms of their hardness to solve, and to determine the applicability of continuous-time quantum algorithms in a portfolio approach, where we take advantage of the variation in the hardness of instances between different algorithms by running them in parallel. We find that, while there are correlations in instance hardness between all of the algorithms considered, they appear weak enough that a portfolio approach would likely be desirable in practice. Our results also show a widening range of hardness of randomly generated instances as the problem size is increased, which demonstrates both the difference in the distribution of hardness at small sizes and the value of a portfolio approach that can reduce the number of extremely hard instances. We identify specific weaknesses of these quantum algorithms that can be overcome with a portfolio approach, such their inability to efficiently solve satisfiable instances (which is easy classically).