论文标题
将量子交替运算符ANSATZ应用于图形匹配问题
Applying the Quantum Alternating Operator Ansatz to the Graph Matching Problem
论文作者
论文摘要
量子交流运算符ANSATZ（QAOA+）框架最近因其在嘈杂的中间规模量子（NISQ）设备上解决离散优化问题的能力而引起了人们的关注，该量子以一种可用于衍生的最差案例保证的方式。我们在此框架中设计了一种技术，以解决图表中最大匹配的一些问题。即使最大匹配是多项式时间可解的，但大多数计数和采样版本都是＃p-hard。 我们设计了一些算法，这些算法会在匹配中生成叠加，从而使我们可以从它们中取样。特别是，当将空状态作为输入为输入时，我们会在所有可能的匹配中获得叠加，而当将W态作为输入时，将在所有最大匹配中进行叠加。 我们的主要结果是，当在2个规范的图上运行时，与我们QAOA+算法的输出状态相对应的匹配的预期大小大于在所有匹配项中从均匀分布中获得的预期匹配大小。该算法使用W-态作为输入，我们证明与使用空匹配作为输入状态相比，该输入状态更好。
The Quantum Alternating Operator Ansatz (QAOA+) framework has recently gained attention due to its ability to solve discrete optimization problems on noisy intermediate-scale quantum (NISQ) devices in a manner that is amenable to derivation of worst-case guarantees. We design a technique in this framework to tackle a few problems over maximal matchings in graphs. Even though maximum matching is polynomial-time solvable, most counting and sampling versions are #P-hard. We design a few algorithms that generates superpositions over matchings allowing us to sample from them. In particular, we get a superposition over all possible matchings when given the empty state as input and a superposition over all maximal matchings when given the W -states as input. Our main result is that the expected size of the matchings corresponding to the output states of our QAOA+ algorithm when ran on a 2-regular graph is greater than the expected matching size obtained from a uniform distribution over all matchings. This algorithm uses a W -state as input and we prove that this input state is better compared to using the empty matching as the input state.
