Figure 6. CX and CXSWAP sequence lengths for selected permutation equivalence classes, with and without intra-qubit spin permutations allowed. Across all topologies, CXSWAP is 22.2% shorter than applying CX and SWAP operations sequentially and is only 7.34% longer on average than CX. For both CX and CXSWAP, allowing permutations reduces the average and maximum sequence length within each equivalence class.