量子绝热算法对正则超图上两个最优化问题随机实例的性能
The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
摘要：
本文研究了量子绝热算法在两个随机组合优化问题3-正则3-XORSAT和3-正则Max-Cut上的性能。与这两个基于子句的优化问题相关联的成本函数是相似的，因为它们都定义在3-正则超图上。对于3-正则3-XORSAT，子句包含三个变量，对于3-正则Max-Cut，子句包含两个变量。我们研究这两个问题的量子绝热算法使用随机的内插哈密顿算子，因此适用于无符号问题的量子蒙特卡罗和量子腔方法。使用这些技术，我们发现，量子绝热算法未能有效地解决这些问题，虽然出于不同的原因。
英文摘要：
In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular Max-Cut. The cost functions associated with these two clause-based optimization problems are similar as they are both defined on 3-regular hypergraphs. For 3-regular 3-XORSAT the clauses contain three variables and for 3-regular Max-Cut the clauses contain two variables. The quantum adiabatic algorithms we study for these two problems use interpolating Hamiltonians which are stoquastic and therefore amenable to sign-problem free quantum Monte Carlo and quantum cavity methods. Using these techniques we find that the quantum adiabatic algorithm fails to solve either of these problems efficiently, although for different reasons.
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。
