Most quantum compiler transformations and qubit allocation techniques to date are either peep-hole focused or rely on sliding windows that depend on a number of external parameters. Thus, global optimization criteria are still lacking. In this paper we explore the synergies and impact of affine loop transformations in the context of qubit allocation and mapping. With this goal in mind, we have implemented a domain specific language and source-to-source compiler for quantum circuits that can be directly described with affine relations. We conduct an extensive evaluation spanning 8 quantum circuits taken from the literature, 3 distinct coupling graphs, 4 affine transformations (including the Pluto dependence distance minimization and Feautrier's minimum latency algorithms), and 4 qubit allocators. Our results demonstrate that affine transformations using global optimization criteria can cooperate effectively in several scenarios with quantum qubit mapping algorithms to reduce the circuit depth, size and allocation time.

中文翻译：

---

探索仿射循环变换在量子位分配中的影响

迄今为止，大多数量子编译器转换和量子位分配技术要么专注于窥视孔，要么依赖于依赖于许多外部参数的滑动窗口。因此，仍然缺乏全局优化标准。在本文中，我们探讨了仿射循环变换在量子位分配和映射的背景下的协同作用和影响。考虑到这一目标，我们为量子电路实现了一种领域特定语言和源到源编译器，可以用仿射关系直接描述。我们对文献中的 8 个量子电路、3 个不同的耦合图、4 个仿射变换（包括 Pluto 依赖距离最小化和 Feautrier 的最小延迟算法）和 4 个量子位分配器进行了广泛的评估。