Mapping Nearest Neighbor Compliant Quantum Circuits Onto a 2-D Hexagonal Architecture

Quantum algorithms can be described as quantum circuits and are supposed to be carried out on an ideal quantum device that is far from current ones. The current quantum devices have a significant limitation on the connectivity between quantum bits. In other words, a quantum bit is only allowed to interact with its nearest neighbors (NNs). In reality, quantum bits have to be placed on a grid, where the connectivity between quantum bits is predefined. The predefined connectivity of a grid further determines the possible range of architectures of a quantum device after the placement of quantum bits. In this article, we propose to place quantum bits based on a 2-D hexagonal architecture rather than a 2-D Cartesian architecture. To validate the effectiveness, we leverage a workflow for mapping NN compliant quantum circuits onto targeting grids, where the workflow consists of a global reordering strategy and a local reordering strategy. With the advantages of the hexagonal grid, the overhead of making quantum circuits NN compliant is reduced significantly compared with the Cartesian grid. We also provide a comprehensive set of ablation analyses to gain a better understanding of the contributions of the components within our workflow. According to the experimental results, when changing the grid type from Cartesian to hexagonal, the global reordering strategy is crucial for small quantum circuits. In contrast, the local reordering strategy is more important than the global reordering strategy for large quantum circuits.