qGDR: A Via-Minimization-Oriented Routing Tool for Large-Scale Superconductive Single-Flux-Quantum Circuits

Single-flux-quantum (SFQ) circuit technologies are promising digital circuit technologies with high-speed and extremely low-power characteristics. However, heavy wire routing tasks are finished either by considerable human effort or by commercial routing tools with few physical considerations for the SFQ circuits. In this paper, we present an integrated global and detailed router for the SFQ circuits, qGDR, which aims at reducing the impedance mismatch during signal transfer by minimizing the total number of used vias. The global router allocates routing resources while minimizing the via usage by a dynamic layer assignment algorithm. The detailed router follows the global routing results to complete the routing task by resorting to a maze routing algorithm. Following the MIT-LL SFQ5ee process technology, qGDR can use only two routing layers to route an 8-bit integer divider with more than 40 000 Josephson junctions in less than one hour.