Window size estimation for nearest neighbour compliant quantumcircuit mapping

In general, quantum circuits permit anytwological qubits tobe combined viaa quantum gate. When these are tobe deployed on locally-connected grid-shaped quantum processors, swap operations are required to make adjacent interacting qubits. Swap insertion algorithms are complex and time-consuming. Windowing limits this complexity by considering onlya subset ofthe circuit's gates when inserting swaps, but hasnotbeen applied tothe latest generation of swap insertion algorithms, nor hasany systematic method been proposed for determining the appropriate window length. This paper showshowoff-line analysis ofswap density across the circuit identifies thresholds for window length which limit increases inthe number of swap gates. When adopted, speed-ups inthe swap insertion process asymptotically approach 100% with the length ofthe circuit, whilst maintaining swap costsat comparable levelstonon-windowed algorithms.