Exploring the Impact of Affine Loop Transformations in Qubit Allocation

Abstract: 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.