Determining the minimal number of swap gates for multi-dimensional nearest neighbor quantum circuits

Motivated by the promises of significant speed-ups for certain problems, quantum computing received significant attention in the past. While much progress has been made in the development of synthesis methods for quantum circuits, new physical developments constantly lead to new constraints to be addressed. The limited interaction distance between the respective qubits (i.e. nearest neighbor optimization) has already been considered intensely. But with the emerge of multi-dimensional quantum architectures, new physical requirements came up for which only a few automatic synthesis solutions exist yet all of them of heuristic nature. In this work, we propose an exact scheme for nearest neighbor optimization in multi-dimensional quantum circuits. Although the complexity of the problem is a serious obstacle, our experimental evaluation shows that the proposed solution is sufficient to allow for a qualitative evaluation of the respective optimization steps. Besides that, this enabled an exact comparison to heuristical results for the first time.