Recently, there has been considerable interest in solving optimization problems by mapping these onto a binary representation, sparked mostly by the use of quantum annealing machines. Such binary representation is reminiscent of a discrete physical two-state system, such as the Ising model. As such, physics-inspired techniques—commonly used in fundamental physics studies—are ideally suited to solve optimization problems in a binary format. While binary representations can be often found for paradigmatic optimization problems, these typically result in k-local higher-order unconstrained binary optimization cost functions. In this work, we discuss the effects of locality reduction needed for the majority of the currently available quantum and quantum-inspired solvers that can only accommodate 2-local (quadratic) cost functions. General locality reduction approaches require the introduction of ancillary variables which cause an overhead over the native problem. Using a parallel tempering Monte Carlo solver on Microsoft Azure Quantum, as well as k-local binary problems with planted solutions, we show that post reduction to a corresponding 2-local representation the problems become considerably harder to solve. We further quantify the increase in computational hardness introduced by the reduction algorithm by measuring the variation of number of variables, statistics of the coefficient values, and the population annealing entropic family size. Our results demonstrate the importance of avoiding locality reduction when solving optimization problems.

最近，通过将这些映射到二进制表示来解决优化问题引起了相当大的兴趣，这主要是由使用量子退火机引起的。这种二进制表示让人联想到离散物理二态系统，例如Ising 模型。因此，受物理学启发的技术——通常用于基础物理学研究——非常适合以二进制格式解决优化问题。虽然通常可以为典型优化问题找到二进制表示，但这些通常会导致k-局部高阶无约束二元优化成本函数。在这项工作中，我们讨论了大多数当前可用的量子和量子启发式求解器所需的局部减少的影响，这些求解器只能容纳 2-局部（二次）成本函数。一般的局部性减少方法需要引入辅助变量，这会导致本地问题的开销。使用 Microsoft Azure Quantum 上的并行调和蒙特卡罗求解器，以及带有植入解的k局部二元问题，我们表明后归约到相应的 2 局部表示问题变得相当难以解决。我们进一步量化了减少算法引入的计算硬度的增加通过测量变量数量的变化、系数值的统计和种群退火熵家庭规模。我们的结果证明了在解决优化问题时避免局部减少的重要性。