arXiv 1601.017442016-01-08quant-phcs.CCcs.DS

QAOA在有界度约束满足问题典型解上的性能

Performance of QAOA on Typical Instances of Constraint Satisfaction Problems with Bounded Degree

Cedric Yen-Yu Lin, Yechao Zhu

备注：: 18 pages

摘要：

我们考虑约束满足问题的有界程度，与一个很好的概念“典型性”，例如，否定的变量在每个约束是独立随机。使用量子近似优化算法（QAOA），我们表明，$ μ+Ω(1/\sqrt{D}) $分数的约束可以满足典型的情况下，与分配有效地产生QAOA。我们这样做是通过表明，平均分数的约束得到满足是$ μ+Ω(1/\sqrt{D}) $，具有小的方差。这里$ μ$是均匀随机分配所满足的分数，而$ D $是每个变量可以出现的约束数。具有典型性的CSP包括Max- $ k $ XOR和Max- $ k $ SAT。我们指出如何可以应用它来确定典型的基态能量的一些本地的哈密顿量。我们也给出了类似的结果的情况下，“没有重叠的约束”，使用量子算法。我们勾勒出经典算法如何可能实现某些部分的结果。

英文摘要：

We consider constraint satisfaction problems of bounded degree, with a good notion of "typicality", e.g. the negation of the variables in each constraint is taken independently at random. Using the quantum approximate optimization algorithm (QAOA), we show that $ μ+Ω(1/\sqrt{D}) $ fraction of the constraints can be satisfied for typical instances, with the assignment efficiently produced by QAOA. We do so by showing that the averaged fraction of constraints being satisfied is $ μ+Ω(1/\sqrt{D}) $, with small variance. Here $ μ$ is the fraction that would be satisfied by a uniformly random assignment, and $ D $ is the number of constraints that each variable can appear. CSPs with typicality include Max-$ k $XOR and Max-$ k $SAT. We point out how it can be applied to determine the typical ground-state energy of some local Hamiltonians. We also give a similar result for instances with "no overlapping constraints", using the quantum algorithm. We sketch how the classical algorithm might achieve some partial result.

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。

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